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This paper focuses on the study of existence of solutions and periodic solutions for a general class of neutral measure functional differential equations (NMFDEs for short) with infinite delay. The relationship between solutions of NMFDEs with infinite delay and solutions of generalized ordinary differential equations is first discussed, based on this the existence, uniqueness and continuous dependence of solutions for NMFDEs with infinite delay are investigated. Then the existence of periodic solutions for the considered equation is also studied and the corresponding sufficient conditions are obtained by fixed-point principle. Finally two examples are given to illustrate the main obtained results. • Study the existence of solutions and periodic solutions for general NMFDEs with infinite delay. • Due to different approaches, assumptions in the main results are more applicable and concise. • Avoid the priori boundedness assumptions on periodic solutions. [ABSTRACT FROM AUTHOR]

This paper investigates the qualitative properties of the solutions for neutral implicit stochastic Hilfer fractional differential equations involving Lévy noise with retarded and advanced arguments. The existence property of the solution of the aforementioned equation is demonstrated by the Mónch condition, and the uniqueness is demonstrated by the remarkable fixed point of Banach. In addition, we examine the Hyers–Ulam (HU) stability of the presented mathematical models. To substantiate our theoretical conclusions, a real-world example is included to illustrate their practical application. [ABSTRACT FROM AUTHOR]

The purpose of this article concerns a type of nonlinear boundary value problem of fractional differential equations with the Caputo derivative. Using the fixed point index theory of condensing mapping in cones, the existence results of positive solutions for such a problem are obtained. [ABSTRACT FROM AUTHOR]

We consider the fully nonlocal diffusion equations with nonnegative L1$L^1$‐data. Based on the approximation and energy methods, we prove the existence and uniqueness of nonnegative entropy solutions for such problems. In particular, our results are valid for the time‐space fractional Laplacian equations. [ABSTRACT FROM AUTHOR]

This study examines a mixed initial-boundary value problem in thermoelastic materials with a double porosity structure, taking into account the effects of microtemperature. The existence of a solution is established by converting the problem into a Cauchy-type problem. Given the complexity of the equations, unknowns, and conditions, we apply contraction semigroup theory within a specific Hilbert space. We prove the existence of a solution using the Lax-Milgram theorem. Additionally, the uniqueness of the solution is demonstrated based on the Lumer-Phillips corollary, which corresponds to the Hille-Yosida theorem. In the final section, we show the continuous dependence of the solution on the mixed initial-boundary value problem for double porous thermoelasticity with microtemperature. [ABSTRACT FROM AUTHOR]

In this paper we consider two classes of nonlinear partial differential equations with the fractional Laplacian, namely $$\begin{align*} \left(-\Delta\right)^{\frac{\alpha}{2}}\left(u^{m} \right) &=u\left|u\right|^{q-1}+w\left(x\right), \quad x\in \mathbb{R}^{N},\\ &\qquad 1\leq m (− Δ) α 2 (u m) = u | u | q − 1 + w (x) , x ∈ R N , 1 ≤ m < q , 0 < α ≤ 2 , N > α and $$\begin{align*} &\frac{\partial^{k}u}{\partial t^{k}}+\left(-\Delta\right)^{\frac{\alpha}{2}}u=u^{q}, \quad \left(x,t\right)\in \mathbb{R}^{N}\times\left(0,+\infty\right),\\ &\qquad k\geq 1, \ 0 ∂ k u ∂ t k + (− Δ) α 2 u = u q , (x , t) ∈ R N × (0 , + ∞) , k ≥ 1 , 0 < α ≤ 2 , N > α. Solutions defined for all $ x\in \mathbb {R}^{N} $ x ∈ R N of the first equation are referred to as entire solutions, while solutions defined for all $ \left (x,t\right)\in \mathbb {R}^{N}\times \left [0,+\infty \right) $ (x , t) ∈ R N × [ 0 , + ∞) of the second equation are referred to as global solutions. Several existence and nonexistence theorems are established over different ranges of q, and thus the respective relations between the existence, nonexistence of solutions for these equations and the index q in the nonlinear terms are obtained. It is illustrated that our results are sharp in cases of m = 1 and k = 1 respectively. In addition, we prove the positivity, symmetry and odevity of solutions we constructed for the first equation with m = 1 associated with the inhomogeneous term w. [ABSTRACT FROM AUTHOR]

This article is to develop a method to solve the boundary value problems of the first-order measure differential equations in the space of bound-ed variation functions. Firstly, we obtain the solution and Green's function by applying the integration by parts. Secondly, the criterion for the existence of solution is given by using fixed point theorem and regularization theory. Finally, an example is provided to validate these conclusions. [ABSTRACT FROM AUTHOR]

In this work, a new solution for the bipolar-fuzzy initial value problem is proposed. This method is obtained by approximating the solution by piece-wise polynomial of order three. The existence and uniqueness of the solution and convergence of the method are discussed in detail. Finally, for more explanation, several numerical examples are solved. [ABSTRACT FROM AUTHOR]

The article investigates a Dirichlet-type problem with conjugation conditions for a degenerate equation of high even order with variable coefficients, including the Riemann–Liouville fractional derivative, in a rectangular region consisting of two subdomains ( y > 0 and y < 0 ), in each of which the equation has various kind.The solution is constructed as a series in terms of eigenfunctions of the one-dimensional problem, the existence of eigenfunctions is proved by the method of the theory of integral equations with symmetric kernels. The theorem of expansion in terms of the system of obtained eigenfunctions is proved. Sufficent conditions are found for boundary functions under which the solution in the form of a series converges uniformly. When justifying the convergence of a series, the problem of "small denominators" arises.This problem has been successfully solved in the article. The uniqueness of the solution is proved by the spectral method. [ABSTRACT FROM AUTHOR]

Christopher Marlowe's Doctor Faustus (1588) intricately explores the interplay of religious motifs, cosmic exploration, and themes related to Space, Heaven, Hell, and repentance. By incorporating biblical and Qur'anic references, Marlowe crafts a compelling narrative that deeply resonates with the human experience. The central character, Faustus, embodies the conflict between good and evil and between human ambition and spiritual limitation. The play's depiction of celestial realms parallels biblical narratives like the 'Tower of Babel' and Qur'anic visions, emphasizing humanity's persistent quest for knowledge and divine understanding. This study examines how Marlowe integrates religious concepts, andangelic and cosmic themes with theological and moral conflicts, highlighting the thematic parallels with sacred narratives from the Bible and the Qur'an. To conclude, Faustus' mythology remains a poignant and thought-provoking narrative that resonates across different cultural and religious contexts. [ABSTRACT FROM AUTHOR]

In this paper, we study a new class of coupled systems of nonlinear generalized fractional differential equations complemented with coupled nonlocal Riemann–Stieltjes and generalized fractional integral boundary conditions. The nonlinearities also include the lower order generalized fractional derivatives of the unknown functions. We apply the Banach contraction mapping principle and Leray–Schauder alternative to derive the desired results. An illustrative example is also discussed. The results presented in this work are novel in the given configuration and yield some new results as special cases (for details, see the Conclusion section). [ABSTRACT FROM AUTHOR]

In this paper, we are concerned with a problem of periodic solution for a second order nonautonomous differential equation with a discontinuity line. Under two types of assumptions, we analyze the geometric properties of solutions respectively. Then by using a fixed point theorem, we obtain several existence criteria of periodic solutions, where the periodic solutions are crossing harmonic and subharmonic solutions. [ABSTRACT FROM AUTHOR]

In this work, we deal with a more general form of fractional Langevin equation. The equation’s nonlinearity term f is relevant to fractional integral and fractional derivative. By using the fixed point theorems, we study the existence and uniqueness of solutions of initial value problem for the nonlinear fractional Langevin equation and obtain some new results. Further, by using the technique of nonlinear functional analysis, we study the stability of Ulam-Hyers, Ulam-Hyers-Rassias and semi-Ulam-Hyers-Rassias for the initial value problem of nonlinear Langevin equation. Finally, some examples are given to show the effectiveness of theoretical results. [ABSTRACT FROM AUTHOR]

This article aims to explore the existence and stability of solutions to differential equations involving a ψ -Hilfer fractional derivative in the Caputo sense, which, compared to classical ψ -Hilfer fractional derivatives (in the Riemann–Liouville sense), provide a clear physical interpretation when dealing with initial conditions. We discovered that the ψ -Hilfer fractional derivative in the Caputo sense can be represented as the inverse operation of the ψ -Riemann–Liouville fractional integral, and used this property to prove the existence of solutions for linear differential equations with a ψ -Hilfer fractional derivative in the Caputo sense. Additionally, we applied Mönch's fixed-point theorem and knowledge of non-compactness measures to demonstrate the existence of solutions for nonlinear differential equations with a ψ -Hilfer fractional derivative in the Caputo sense, and further discussed the Ulam–Hyers–Rassias stability and semi-Ulam–Hyers–Rassias stability of these solutions. Finally, we illustrated our results through case studies. [ABSTRACT FROM AUTHOR]

This paper deals with some existence and uniqueness results for a class of problems systems for nonlinear k$$ k $$‐generalized ψ$$ \psi $$‐Hilfer fractional differential equations with periodic conditions. The arguments are based on Mawhin's coincidence degree theory. Furthermore, an illustration is presented to demonstrate the plausibility of our results. [ABSTRACT FROM AUTHOR]

The Article examines the world view evolution of Father Sergius Bulgakov; namely, the stage of his radical reorientation to the problems of philosophical idealism and religious metaphysics. That world view is shaped by a tension between his mystical spiritual experiences described in his diary and jos attempts to externalize them as Christian politics. He articulates the relationship between philosophy and religion as an antinomy and therefore cannot be resolved only through rationalization. It demands for the orthodox consciousness the justification of philosophy in the light of religion. Overcoming the autonomy of reason is possible due to the rooting of philosophical reason in a specific religious experience. It is in the religious existential experience of the transcending subject that it is possible to go beyond the limits of empirical existence and overcome limitations of the secular autonomous reason. Thus, Bulgakov's views are largely in tune with European existential philosophy in interpreting the nature of philosophy as creativity rooted in the deepest, pre-rational foundations of human existence. [ABSTRACT FROM AUTHOR]

In this paper, we consider a class of fractional Schrödinger–Poisson systems (− Δ) s u + λ V (x) u + ϕ u = f (u) + | u | 2 s * − 2 u and (− Δ) t ϕ = u 2 in R 3 , where s , t ∈ (0 , 1) with 2 s + 2 t > 3 , λ > 0 denotes a parameter, V : R 3 → R admits a potential well Ω ≜ int V − 1 (0) and 2 s * ≜ 6 3 − 2 s is the fractional Sobolev critical exponent. Given some reasonable assumptions as to the potential V and the nonlinearity f, with the help of a constrained manifold argument, we conclude the existence of positive ground state solutions for some sufficiently large λ. Upon relaxing the restrictions on V and f, we utilize the minimax technique to show that the system has a positive mountain-pass type by introducing some analytic tricks. Moreover, we investigate the asymptotical behavior of the obtained solutions when λ → + ∞ . [ABSTRACT FROM AUTHOR]

I consider a class of dynamic Bayesian games in which types evolve stochastically according to a first-order Markov process on a continuous type space. Types are privately informed, but they become public together with actions when payoffs are obtained, resulting in a delayed information revelation. In this environment, I show that there exists a stationary Bayesian–Markov equilibrium in which a player's strategy maps a tuple of the previous type and action profiles and the player's current type to a mixed action. The existence can be extended to K-periodic revelation. I also offer a computational algorithm to find an equilibrium. [ABSTRACT FROM AUTHOR]

In this paper, we focus on the existence of positive periodic solutions of generalized Leslie–Gower-type population models. Using the topological degree, we provide sufficient conditions to demonstrate the existence of positive periodic solutions to the considered models. It is interesting that the positive periodic solutions in this paper are general positive functions, not e exponential functions, which generalizes and improves the existing results. We note that due to the symmetrical property of periodic solutions, the results of this paper provide a deeper understanding of the periodic behavior of biological populations. Two numerical examples show the effectiveness of our main results. [ABSTRACT FROM AUTHOR]

This work studies an inhomogeneous generalized Hartree equation with inverse square potential. The purpose is to prove the existence and strong instability of inter-critical standing waves. This means that there are infinitely many data near to the ground state, such that the associated solution blows-up in finite time. The proof combines a variational analysis with the standard variance identity. The challenge is to deal with three difficulties: the singular potential | x | − 2 , an inhomogeneous term | x | − λ , and a non-local source term. [ABSTRACT FROM AUTHOR]

We will give a new proof of the existence of non-compact homothetic solitons of the inverse mean curvature flow in ℝ n × ℝ , n ≥ 2 , of the form (r , y ⁢ (r)) or (r ⁢ (y) , y) , where r = | x | , x ∈ ℝ n , is the radially symmetric coordinate and y ∈ ℝ . More precisely for any 1 n < λ < 1 n - 1 and μ < 0 , we will give a new proof of the existence of a unique solution r ⁢ (y) ∈ C 2 ⁢ (μ , ∞) ∩ C ⁢ ([ μ , ∞)) of the equation r y ⁢ y ⁢ (y) 1 + r y ⁢ (y) 2 = n - 1 r ⁢ (y) - 1 + r y ⁢ (y) 2 λ ⁢ (r ⁢ (y) - y ⁢ r y ⁢ (y) ) , r ⁢ (y) > 0 , in (μ , ∞) which satisfies r ⁢ (μ) = 0 and r y ⁢ (μ) = lim y ↘ μ ⁡ r y ⁢ (y) = + ∞ . We prove that there exist constants y 2 > y 1 > 0 such that r y ⁢ (y) > 0 for any μ < y < y 1 , r y ⁢ (y 1) = 0 , r y ⁢ (y) < 0 for any y > y 1 , r y ⁢ y ⁢ (y) < 0 for any μ < y < y 2 , r y ⁢ y ⁢ (y 2) = 0 and r y ⁢ y ⁢ (y) > 0 for any y > y 2 . Moreover, lim y → + ∞ ⁡ r ⁢ (y) = 0 and lim y → + ∞ ⁡ y ⁢ r y ⁢ (y) = 0 . [ABSTRACT FROM AUTHOR]

We investigate a model for the accretive growth of an elastic solid. The reference configuration of the body is accreted in its normal direction, with space- and deformation-dependent accretion rate. The time-dependent reference configuration is identified via the level sets of the unique viscosity solution of a suitable generalized eikonal equation. After proving the global-in-time well-posedness of the quasistatic equilibrium under prescribed growth, we prove the existence of a local-in-time solution for the coupled equilibrium-growth problem, where both mechanical displacement and time-evolving set are unknown. A distinctive challenge is the limited regularity of the growing body, which calls for proving a new uniform Korn inequality. [ABSTRACT FROM AUTHOR]

This paper is devoted to solving a reflected backward stochastic differential equation (BSDE in short) with one continuous barrier and a quasi-linear growth generator g, which has a linear growth in (y, z), except the upper direction in case of y < 0, and is more general than the usual linear growth generator. By showing the convergence of a penalization scheme we prove existence and comparison theorem of the minimal Lp (p > 1) solutions for the reflected BSDEs. We also prove that the minimal Lp solution can be approximated by a sequence of Lp solutions of certain reflected BSDEs with Lipschitz generators. [ABSTRACT FROM AUTHOR]

The existence of the Sanskrit language, which is so amazing with its various scholarships, both Paravidyā and Aparavidyā, has made a major contribution to world culture and the archipelago. In Bali, Kārakam's knowledge is written in a horizontal sheet, with the title Lontar Kārakasaṅgrahaḥ, which until now has only been studied by foreign researchers such as Silvain Levy and J Gonda. However, until now the public did not know about its existence and knowledge. This qualitative research aims to identify and describe the Existence of Lontar Kārakasaṅgrahaḥ as a Kārakam Guide in Sanskrit Grammar. Primary data sources are observation on Lontar Kārakasaṅgrahaḥ as well as information from experts as well as secondary data both from other supporting books. Based on the results of the research and discussion, it was found that: (1) The Lontar form of Kārakasaṅgrahaḥ consists of 21 stanzas of Kārika written in Balinese script with an introduction to Sanskrit, explaining about 6 Kārakam namely Kartā, Karma, Karaṇam, Sampradānam, Apādānam and Ādhikaraṇam and śeṣe and the relationship with use the 7 vibhaktiḥ namelyPrathamāvibhaktiḥ, Dvitīyāvibhaktiḥ, Tṛtī yavibhaktiḥ, Caturthavibhaktiḥ, Pañcamavibhaktiḥ Ṣaṣṭhavibhaktiḥ, Saptamivibhaktiḥ and Sambhodanam. (2) The existence of the use of Kārakam is reflected in the findings of various local Sanskrit literary works in the form of Padya (sloka) and Padya (prose) found with strong Kārakam compositions. [ABSTRACT FROM AUTHOR]

When addressing a decision making problem with incomplete preference relations, missing information could be estimated by proposing an optimization model. The previous studies always focus on a unique solution to optimization models through a software program. But theoretical and simulation investigations of multiple solutions are seldom considered. This paper investigates the existence of multiple solutions to an optimization model and proposes a simulation procedure. First, an optimization model is recalled for completing incomplete fuzzy preference relations. It is the first time to theoretically prove the existence of multiple solutions to the optimization model under various incomplete entries. The obtained results reveal that the optimal solution to an optimization model may be an interval value, which is dependent on the number and position of missing entries in an incomplete fuzzy preference relation. The idea of multiple solutions is further extended to the situation where an intransitive fuzzy preference relation should be adjusted to a weakly transitive matrix. Second, multiple solutions to the optimization model are simulated using the quantum-behaved particle swarm optimization algorithm. It is found that multiple solutions do appear under some conditions by only running the algorithm for multiple times. Finally, the impact of multiple solutions on the optimal alternative(s) of a decision making problem is analyzed by comparing with the existing studies. The result shows that the existence of multiple solutions reflects the uncertainty of optimization models, which is of concerns to propose an effective decision-making model. [ABSTRACT FROM AUTHOR]

The primary aim of this article is to explore the approximate controllability of second-order impulsive hemivariational inequalities with initial conditions in Hilbert space. The mild solution was initially derived using the properties of the cosine and sine family of operators, Clarke's subdifferential, and the fact that the related linear equation has an evolution operator. The results of the approximate controllability of the considered systems are then taken into account using the fixed-point theorem method. An application is provided to support our theoretical findings. [ABSTRACT FROM AUTHOR]

This work studies a coupled non-linear Schrödinger system with a singular source term. First, we investigate the question of the local existence of solutions. Second, one proves the existence of global solutions which scatter in some Sobolev spaces. Finally, one establishes the existence of non-global solutions. The main difficulty here is to overcome the regularity problem in the non-linearity. Indeed, because of the singularity of the source term, the classical contraction method in the energy space fails in such a regime. So, this paper is to fill such a gap in the literature. The argument follows ideas in T. Cazenave and I. Naumkin (Comm. Contemp. Math. , 19 (2017), 1650038). This consists to remark that the singularity problem is only near the origin. So, one needs to impose that the solution stays away from zero. This is not trivial, since there is no maximum principle for the Schrödinger equation. The existence of global solutions which scatter follows with the pseudo-conformal transformation via the existence of local solutions. Finally, the existence of non-global solutions follows with the classical variance method. [ABSTRACT FROM AUTHOR]

This paper explores a fractional integro-differential equation with boundary conditions that incorporate the Hilfer-Hadamard fractional derivative. We model the RLC circuit using fractional calculus and define weighted spaces of continuous functions. The existence and uniqueness of solutions are established, along with their Ulam-Hyers and Ulam-Hyers-Rassias stability. Our analysis employs Schaefer's fixed-point theorem and Banach's contraction principle. An illustrative example is presented to validate our findings. [ABSTRACT FROM AUTHOR]

This paper investigates a doubly haptotactic cross-diffusion system with $ p $-Laplacian diffusion. Under Neumann boundary conditions in a bounded domain $ \Omega \subset \mathbb{R}^2 $ with smooth boundary, it is proved that if $ p>2 $ for all sufficiently smooth initial data, the model possesses at least one global weak solution. [ABSTRACT FROM AUTHOR]

This paper aims to investigate the existence and uniqueness of solutions for a sixth‐order differential equation involving nonlocal and integral boundary conditions. Firstly, we obtain the properties of the relevant Green's functions. The existence result of at least one nontrivial solution is obtained by applying the Krasnoselskii–Zabreiko fixed point theorem. Moreover, we also establish the existence of unique solution to the considered problem via Hölder and Minkowski inequalities and Rus's theorem. Finally, two numerical examples are included to show the applicability of our main results. [ABSTRACT FROM AUTHOR]

Existence, non-existence, and uniqueness of mass-conserving weak solutions to the continuous collision-induced nonlinear fragmentation equations are established for the collision kernels Φ satisfying Φ (x , y) = x λ 1 y λ 2 + y λ 1 x λ 2 , (x , y) ∈ (0 , ∞) 2 , with λ 1 ≤ λ 2 ≤ 1 , and non-integrable fragment daughter distributions. In particular, global existence of mass-conserving weak solutions is shown when 1 ≤ λ : = λ 1 + λ 2 ≤ 2 with λ 1 ≥ k 0 , the parameter k 0 ∈ (0 , 1) being related to the non-integrability of the fragment daughter distribution. The existence of at least one mass-conserving weak solution is also demonstrated when 2 k 0 ≤ λ < 1 with λ 1 ≥ k 0 but its maximal existence time is shown to be finite. Uniqueness is also established in both cases. The last result deals with the non-existence of mass-conserving weak solutions, even on a small time interval, for power law fragment daughter distribution when λ 1 < k 0. It is worth mentioning that the previous literature on the nonlinear fragmentation equation does not treat non-integrable fragment daughter distribution functions. [ABSTRACT FROM AUTHOR]

In this paper, we prove that under weak assumptions on the reaction terms and diffusion coefficients, a positive solution exists for a one-dimensional case and a positive radial solution to a multidimensional case of a nonlocal elliptic problem. Additionally, we establish the uniqueness of the solution, with the fixed point theorem being the primary tool employed. Our results are new and generalize several existing results. [ABSTRACT FROM AUTHOR]

The main focus of this manuscript is to study an impulsive fractional integro‐differential equation with delay and Caputo fractional derivative. The existence solution of such a class of fractional differential equations is discussed for linear and nonlinear case with the help of direct integral method. Moreover, Banach's fixed point theorem and Schaefer's fixed point theorem are use to discuss the uniqueness and at least one solution of the said fractional differential equations, respectively. Some hypothesis and inequalities are utilize to present four different types of Hyers–Ulam stability of the mentioned impulsive integro‐differential equation. Example is provide for the illustration of main results. [ABSTRACT FROM AUTHOR]

This paper explores an inverse problem pertaining to the determination of a source function in non‐divergence parabolic equations, where the solution is known at a discrete set of points. Being different from other ordinary inverse source problems, which are often dependent on only one variable, the unknown coefficient in this paper not only depends on the space variable x$$ x $$ but also depends on the time t$$ t $$. On the basis of the optimal control framework, the existence of the optimal solution of the control function is proved. The necessary conditions to be satisfied by the optimal solution are given. The convergence of the optimal solution when the mesh parameters tend to zero is obtained. The conjugate gradient method is applied to the inverse problem and some numerical results are presented for various typical test examples. [ABSTRACT FROM AUTHOR]

AbstractThis paper is devoted to studying the coupled system of multiparameter k-Hessian equationswhere B = {x ∈ ℝn : |x| < 1}, λ1, λ2 are positive parameters, ρi(i = 1, 2) is singular near the boundary ∂B, fi(i = 1, 2) satisfies a combined superlinear condition at ∞. Employing the fixed point theorem of Krasnosel’skii type in Banach space, the existence and multiplicity of nontrivial radial solutions are established. In particular, the dependence of the solutions on the parameters λ1, λ2 is also discussed. Finally, we study the nonexistence results of nontrivial radial solutions for the case λ1, λ2 ≫ 1. [ABSTRACT FROM AUTHOR]

In this paper, we consider the Patlak-Keller-Segel-Navier-Stokes (PKS-NS) system in a three-dimensional bounded domain with general nonequilibrium Dirichlet boundary conditions, which was proposed by Gong and He [SIAM J. Math. Anal., 53 (2021), pp. 2925-2956]. First, we prove the existence of smooth solutions to the boundary value problem for the steady PKS-NS system and obtain two boundary controls on the solutions; namely, the nonnegativity of n can be determined by its positivity at the boundary, and the nonzeroness of u can be determined by the boundary values of n and c. Second, we prove the existence and uniqueness of locally smooth solutions to the initial boundary value problem for the PKS-NS system with boundary values independent on time; in particular, n preserves the nonnegative of its initial data. In addition, we obtain a necessary and sufficient condition with respect to the global regular solutions. Finally, it should be pointed out that the corresponding results of this paper also hold for the two-dimensional bounded domain and for the Patlak-Keller-Segel-Stokes system. [ABSTRACT FROM AUTHOR]

The original KWC system is widely used in materials science. It was proposed in [R. Kobayashi, J. A. Warren, and W. C. Carter, Phys. D, 140 (2000), pp. 141--150] and is based on the phase field model of planar grain boundary motion. This model suffers from two key challenges. First, it is difficult to establish its relation to physics, in particular a variational model. Second, it lacks uniqueness. The former has been recently studied within the realm of BV theory. The latter only holds under various simplifications. This article introduces a pseudo-parabolic version of the KWC system. A direct relationship with variational model (as gradient flow) and uniqueness are established without making any unrealistic simplifications. Namely, this is the first KWC system which is both physically and mathematically valid. The proposed model overcomes the well-known open issues. [ABSTRACT FROM AUTHOR]

We introduce a class of fully nonlinear mean field games posed in [0,T] × Rd. We justify that they are related to controlled local or nonlocal diffusions, and more generally in our setting, to a new control interpretation involving time change rates of stochastic (L\'evy) processes. The main results are the existence and uniqueness of solutions under general assumptions. These results are applied to nondegenerate equations--including both local second-order and nonlocal with fractional Laplacians. Uniqueness holds under the monotonicity of couplings and convexity of the Hamiltonian, but neither monotonicity nor convexity need to be strict. We consider a rich class of nonlocal operators and processes and develop tools to work in the whole space without explicit moment assumptions. [ABSTRACT FROM AUTHOR]

In this article discusses, the evidential nature of the knowledge that qualifies one as a human being and the existential and epistemic processes of being responsible will be discussed from a Muʿtazilite perspective. What are the intrinsic and cognitive qualities that make human beings knowers? How should the intellect be understood as evidence and its functional contribution to the process of gaining knowledge from evidence? To what extent is the activity of the subject's realized in the process of intellect, evidence, and knowledge? How can the minimum cognitive conditions that make human beings responsible be explained in relation to the nature of the obligation (taklif) Assuming that every human being, by virtue of his/her nature and rational faculties, is capable of reaching the level of knowledge that is the source of responsibility, what justifies moral retribution (punishment) in the case of failure despite the existence of this capacity? Seeking answers to questions like these is the main interest of this article. In Muʿtazilite theology, not recognizing God and His superior qualities, and not completing the process of obligation for a virtuous life means that the individual will face a consequence proportional to his level of belief and morality. Moreover, man can use his/her intellect to investigate the causes and reasons of things, to understand what the evidence points to, and to complete the epistemic process that leads to the unknown. By nature, man knows himself/herself, is aware of the external world, wills, perceives, has a priori knowledge, is willing to think, is aware of the evidence, can understand what is said, knows the causes of his actions, and the nature of moral values. Therefore, this article will examine the initial principles that make human beings responsible and the cognitive limits that arise from human nature. The stages of human responsibility from physical development to intellectual maturity will be discussed from a Muʿtazilite perspective with a descriptive method. After mentioning the basic nature of the a priori knowledge that makes man responsible as an intelligent being, the existential and cognitive processes that require responsibility will be analyzed. Since the article is not a interfactional comparison, the main issue will be analyzed on the axis of Mu'tazila. For this reason, the main issue will be examined around a theme in which the intellect and moral nature are at the center, without giving space to a detailed lexical and terminological conceptual analysis. The article focuses on the physical factors that make human beings responsible, the lowest level of knowledge, the qualities of knowledge that require being responsible, and the intellectual and moral process of obligation. The relationship of knowledge about God to existential and cognitive processes is determined with categorical distinctions in order to ensure the originality sought. [ABSTRACT FROM AUTHOR]

The study involves a mathematical analysis of the Brusselator system on a convex bounded three-dimensional open domain, considering Neumann boundary conditions. We establish the global existence and uniqueness of the strong solution for this system. Achieving high regularity for the strong solution requires stringent conditions on the initial data. The study demonstrates the continuous dependence of the solution on the initial conditions. [ABSTRACT FROM AUTHOR]

This paper is devoted to the study of a fractional q-difference equation involving dual hybrid terms and equipped with nonlocal multipoint and Riemann-Liouville fractional q-integral boundary conditions. Applying a fixed point approach, we investigate the existence criteria for solutions to the given problem. Examples are constructed for illustrating the obtained results. We emphasize that our results are new in the given configuration, and some new results follow as special cases of the present ones. [ABSTRACT FROM AUTHOR]

In 1947, Emmanuel Levinas published a short essay entitled “Being Jewish” (“Être juif”) in the magazine Confluences. Starting from a reflection on “the Jewish question” or “problem” (Judenfrage), Levinas inquiries into the “reason for being” or justification of Jewish existence. His essay has been the subject of a reappropriation by some interpreters who make Levinas’s claim of “being Jewish” the fulcrum of an ontological conversion or Heideggerianization of his thought. This paper aims to critically analyze one of these hermeneutic perspectives, that of Sarah Hammerschlag, addressing two decisive questions opened by Levinas’s text: Jewish identity and Judaism in history. An alternative approach to the 1947 text is set out, which involves another way of understanding the meaning of Levinas’s analysis of being Jewish. [ABSTRACT FROM AUTHOR]

We explore the existence, uniqueness, and multiplicity of positive solutions to a system of Hadamard fractional differential equations that contain fractional integral terms. Defined on a finite interval, this system is subject to general coupled nonlocal boundary conditions encompassing Riemann–Stieltjes integrals and Hadamard fractional derivatives. To establish the main results, we employ several fixed-point theorems, namely the Banach contraction mapping principle, the Schauder fixed-point theorem, the Leggett–Williams fixed-point theorem, and the Guo–Krasnosel'skii fixed-point theorem. [ABSTRACT FROM AUTHOR]

According to Carolyne Larrington, legends of the past 'offer particular kinds of answers – beautiful and mysterious answers... – to very large questions through a kind of metaphorical thinking... which, in their stripped-down clarity, show us what's really important in an unfamiliar light'. The claim that 'what is really important [is disclosed] by casting it in an unfamiliar light' I take into a philosophical engagement with the figure of the ghost. Far from being of dubious interest for the philosopher of religion, the continuing fascination with ghosts and hauntings offers promising ground for the discussion of religion, for the study of ghosts holds out the possibility of engaging with the wonder and terror of the human condition. The figure of something that is dead yet alive is a creative representation of the fact that we who are alive are also mortal, destined to die. The resulting confrontation with death arouses anxiety, but also has the potential to enrich life. The wisdom of the ghost thus enables the possibility of returning philosophy of religion to the great themes of human existence – birth, suffering, loss, and death – which provide rich resources for understanding religion and its relation to the experience of being human. [ABSTRACT FROM AUTHOR]

The characterization of external or mental occurrence " is a famous criterion for dividing rational things into "primary, secondary logical, and secondary philosophical." This criterion, in addition to being semantically ambiguous, implies a two-sided meaning, i.e. relying on "accidentoccurrence" or "quality-qualified," while such duality is not hidden in the concept of "intelligible" and especially "first intelligibles". The division of intelligible things into primary and secondary has another more precedent criterion, which is the precedence and lateness in rationality. In this criterion, primary intelligible things refer to essential concepts and external concomitants, and secondary intelligible things refer to logical concepts and internal concomitants, but philosophical concepts do not have a clear place in this classification. Shihab al-Din Suhrawardi placed philosophical concepts under secondary intelligibles. After him, some others opposed the exclusive enumeration of philosophical intelligible things, but the thinking of Asalat alMahwiyat ( fundamentality of whatness ) led to placing these intelligible things in a limbo of external and mental attributes and deviating from the old criterion. Mulla Sadra considered mental attributes and external concomitants impossible and proved the externality of philosophical concepts. Of course, considering the various meanings of "existence," its position in the first and second rationality differ. Existence in the sense of "truth of existence" is not secondary rational. However, since externality is associated with existence and it is not possible to consider the "general and abstract concept of existence" as the same as external existence, and this meaning is derived from the nature of rationality, it is secondary rational. Nevertheless, since this meaning implies externality, the concurrence of secondary rationality and mentality must be denied. [ABSTRACT FROM AUTHOR]

The subject of this study is a nonlinear viscoelastic plate equation with variable exponents and a general source term. Through the application of the Faedo–Galerkin approximation method and a fixed point theorem under appropriate assumptions, we proved the existence of weak solutions. [ABSTRACT FROM AUTHOR]

This dialogue, taking place between Prof. Whether and Prof. What, focuses on the nature of the relationship between ontology, conceived as the branch of philosophy concerned with the question of what entities exist, and metaphysics, conceived as the complementary part of philosophy that seeks to explain, of those entities, what they are. Most philosophers claim that it is not possible to address the first question without at the same time addressing the second, since knowing whether an entity exists requires knowing what that entity is. Prof. Whether argues against this popular position and offers a detailed analysis of the idea according to which it is possible to do ontology without engaging in metaphysics. Prof. Whether and Prof. What agree that, rather than being merely possible, in some cases it is, for methodological reasons, even preferable to start with a metaphysics-free ontology, postponing any inquiry concerning the nature of the entities included in the ontological inventory to a later stage. However, Prof. What notes that it is not always possible to do ontology without metaphysics, because there are certain kinds of entities, such as universals and possible worlds, that necessarily need a prior metaphysical characterization. [ABSTRACT FROM AUTHOR]

In this paper, we consider the critical problem involving local and nonlocal operator with critical exponent under the zero mass case. First, we establish the continuous and compactness Sobolev embedding results. Second, we establish the non-existence result by Pohožaev identity. Finally, we prove the existence results for upper-crtical and lower-crtical cases via Sobolev embedding theorem, Mountain-pass theorem and Nehari manifold. [ABSTRACT FROM AUTHOR]

In this paper, we study the discrete Kirchhoff–Choquard equation - a + b ∫ Z 3 | ∇ u | 2 d μ Δ u + V (x) u = R α ∗ F (u) f (u) , x ∈ Z 3 , where a , b > 0 , α ∈ (0 , 3) are constants and R α is the Green’s function of the discrete fractional Laplacian that behaves as the Riesz potential. Under some suitable assumptions on V and f, we prove the existence of nontrivial solutions and ground state solutions respectively by variational methods. [ABSTRACT FROM AUTHOR]

In this paper, we study the strong Nash equilibria of games with additively coupled utilities and a continuum of players. We first prove the existence of strong Nash equilibria for games with additively coupled utilities and finitely many players. Furthermore, we introduce the notion of weak strong Nash equilibria for games with additively coupled utilities and a continuum of players, and prove the existence theorem. Our paper develops the work of strong Nash equilibria. [ABSTRACT FROM AUTHOR]