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The objective of this study is to determine whether the existence of shared sets S containing both meromorphic (entire) functions and their higher derivatives, as well as powers of meromorphic functions and their differential polynomials, could result in uniqueness. The main focus is on determining the precise solutions to various differential equations. This problem is being studied in a broader context, specifically in set sharing. [ABSTRACT FROM AUTHOR]

The system of Brusselator-type reaction-diffusion equations (RDs) on open bounded convex domains 풟 ⊂ ℝ d (d ≤ 3) with Robin boundary conditions (Rbcs) has been mathematically analyzed. The Faedo–Galerkin approach is used to demonstrate the global existence and uniqueness of a weak solution to the system. The weak solution's higher regularity findings are constructed under more regular conditions on the initial data. In addition, continuous dependence on the initial conditions has been proved. [ABSTRACT FROM AUTHOR]

We study the local and global existence and uniqueness of a strict solution for a general class of abstract explicit neutral equations with state-dependent delay. Some examples on explicit partial neutral differential equations with state dependent delay are presented. [ABSTRACT FROM AUTHOR]

In correspondence analysis (CA), the rows and columns of a contingency table are optimally represented in a k -dimensional approximation, where it is common to set k = 3 (which includes a so-called trivial dimension). Since CA is a dimension reduction technique, we might expect that the k -dimensional approximation is not unique, i.e. there exist several contingency tables with the same k -dimensional approximation. Interestingly, Van de Velden et al. [17] find in their computational experiments that 3-dimensional CA solutions are unique up to rotation, which leads to the question whether this is always the case. We show that k -dimensional CA solutions are not necessarily unique. That is, two distinct contingency tables may have the same k -dimensional approximation. We present necessary and sufficient conditions for the non-uniqueness of CA solutions, which hold for any value of k. Based on our sufficient conditions, we present a procedure to generate contingency tables with the same k -dimensional solution. Finally, we note that it is difficult to satisfy the necessary conditions, which suggests that CA solutions are most likely unique in practice. [ABSTRACT FROM AUTHOR]

This present paper is dedicated to the study of the Cauchy problem of the two-dimensional Euler-Boussinesq-Bénard equations which couple the incompressible Euler equations for the velocity and a transport equation with critical dissipation for the temperature. We show that there is a global unique solution to this model with Yudovich's type data. This settles the global regularity problem which was remarked by Wu and Xue (2012) [44]. [ABSTRACT FROM AUTHOR]

In this paper, we focus on the following Schrödinger–Kirchhoff‐type problem with fourth‐order dispersion: γΔ2u−a+b∫ℝN|∇u|2dxΔu+u=|u|2σu,x∈ℝN,u∈H2(ℝN),$$ \left\{\begin{array}{c}\gamma {\Delta}&amp;#x0005E;2u-\left(a&amp;#x0002B;b{\int}_{{\mathrm{\mathbb{R}}}&amp;#x0005E;N}{\left&amp;#x0007C;\nabla u\right&amp;#x0007C;}&amp;#x0005E;2\mathrm{d}x\right)\Delta u&amp;#x0002B;u&amp;#x0003D;{\left&amp;#x0007C;u\right&amp;#x0007C;}&amp;#x0005E;{2\sigma }u,x\in {\mathrm{\mathbb{R}}}&amp;#x0005E;N,\\ {}u\in {H}&amp;#x0005E;2\left({\mathrm{\mathbb{R}}}&amp;#x0005E;N\right),\end{array}\right. $$ where γ,a,b>0$$ \gamma, a,b&gt;0 $$ are constants and σ≥1$$ \sigma \ge 1 $$. We make use of Nehari manifold technique together with concentration‐compactness principle to prove that the above equation has at least a ground state solution for 1≤σ<4N−4$$ 1\le \sigma &lt;\frac{4}{N-4} $$ if N=5$$ N&amp;#x0003D;5 $$, 6, and 7, and for 1≤σ<+∞$$ 1\le \sigma &lt;&amp;#x0002B;\infty $$ if N≤4$$ N\le 4 $$. Moreover, we also investigate the asymptotic behaviors of ground state solutions when some coefficients tend to zero. Among them, a uniqueness result about ground state solutions is obtained by implicit function theorem, and a blow‐up result is established by Pohozaev identity if dimension N=3$$ N&amp;#x0003D;3 $$. [ABSTRACT FROM AUTHOR]

We deal with the following singular perturbation Kirchhoff equation: − ϵ 2 a + ϵ b ∫ R 3 | ∇ u | 2 d y Δ u + Q (y) u = | u | p − 1 u , u ∈ H 1 (R 3) , where constants a , b , ϵ > 0 and 1 < p < 5 . In this paper, we prove the uniqueness of the concentrated solutions under some suitable assumptions on asymptotic behaviors of Q (y) and its first derivatives by using a type of Pohozaev identity for a small enough ϵ. To some extent, our result exhibits a new phenomenon for a kind of Q (x) which allows for different orders in different directions. [ABSTRACT FROM AUTHOR]

In this research, a comprehensive stochastic model was developed to analyze the transmission dynamics of methicillin-resistant Staphylococcus aureus (MRSA) in both hospital-acquired and community-acquired contexts. The study explored the existence and uniqueness of solutions and established the presence of a global solution. The investigation focused on assessing the boundedness, extinction, and persistence of MRSA strains in terms of their means. The analysis of the model revealed a noteworthy phenomenon known as competitive exclusion, where the community-acquired MRSA strain gradually out-competes the hospital-acquired strain within hospital settings. In conclusion, effective interventions and preventive measures, such as improving hand hygiene compliance, implementing decolonization strategies, and enhancing disinfection rates, emerge as critical factors in controlling the transmission of these strains within hospital environments. [ABSTRACT FROM AUTHOR]

To study the dynamical system, it is necessary to formulate the mathematical model to understand the dynamics of various diseases which are spread in the world wide. The objective of the research study is to assess the early diagnosis and treatment of cholera virus by implementing remedial methods with and without the use of drugs. A mathematical model is built with the hypothesis of strengthening the immune system, and a ABC operator is employed to turn the model into a fractional-order model. A newly developed system SEIBR, which is examined both qualitatively and quantitatively to determine its stable position as well as the verification of flip bifurcation has been made for developed system. The local stability of this model has been explored concerning limited observations, a fundamental aspect of epidemic models. We have derived the reproductive number using next generation method, denoted as “ R 0 ”, to analyze its impact rate across various sub-compartments, which serves as a critical determinant of its community-wide transmission rate. The sensitivity analysis has been verified according to its each parameters to identify that how much rate of change of parameters are sensitive. Atangana–Toufik scheme is employed to find the solution for the developed system using different fractional values which is advanced tool for reliable bounded solution. Also the error analysis has been made for developed scheme. Simulations have been made to see the real behavior and effects of cholera disease with early detection and treatment by implementing remedial methods without the use of drugs in the community. Also identify the real situation the spread of cholera disease after implementing remedial methods with and without the use of drugs. Such type of investigation will be useful to investigate the spread of virus as well as helpful in developing control strategies from our justified outcomes. [ABSTRACT FROM AUTHOR]

General geostatistical models are powerful tools for analyzing spatial datasets. A two‐step estimation based on the likelihood function is widely used by researchers, but several theoretical and computational challenges remain to be addressed. First, it is unclear whether there is a unique global maximizer of the log‐likelihood function, a seemingly simple but theoretically challenging question. The second challenge is the convexity of the log‐likelihood function. Besides these two challenges in maximizing the likelihood function, we also study the theoretical property of the two‐step estimation. Unlike many previous works, our results can apply to the non‐twice differentiable covariance functions. In the simulation studies, three optimization algorithms are evaluated in terms of maximizing the log‐likelihood functions. [ABSTRACT FROM AUTHOR]

We consider a nonlinear Dirichlet problem driven by the (p (z) , q) -Laplacian and with a logistic reaction of the equidiffusive type. Under a nonlinearity condition on a quotient map, we show existence and uniqueness of positive solutions and the result is global in parameter λ. If the monotonicity condition on the quotient map is not true, we can no longer guarantee uniqueness, but we can show the existence of a minimal solution u λ * and establish the monotonicity of the map λ ⟼ u λ * and its asymptotic behaviour as the parameter λ decreases to the critical value λ ^ 1 (q) > 0 (the principal eigenvalue of (− Δ q , W 0 1 , q (Ω)) ). [ABSTRACT FROM AUTHOR]

In this paper, we present sufficient conditions for Hyers-Ulam-Rassias stability of nonlinear implicit higher-order Volterra-type integrodifferential equations from above on unbounded time scales. These new sufficient conditions result by reducing Volterra-type integrodifferential equations to Volterra-type integral equations, using the Banach fixed point theorem, and by applying an appropriate Bielecki type norm, the Lipschitz type functions, where Lipschitz coefficient is replaced by unbounded rd-continuous function. [ABSTRACT FROM AUTHOR]

We are investigating the existence of solutions to a system of two fractional q -difference equations containing fractional q -integral terms, subject to multi-point boundary conditions that encompass q -derivatives and fractional q -derivatives of different orders. In our main results, we rely on various fixed point theorems, such as the Leray–Schauder nonlinear alternative, the Schaefer fixed point theorem, the Krasnosel'skii fixed point theorem for the sum of two operators, and the Banach contraction mapping principle. Finally, several examples are provided to illustrate our findings. [ABSTRACT FROM AUTHOR]

This paper combines the concept of an arbitrary binary connection with the widely recognized principle of θ -contraction to investigate the innovative features of vector-valued metric spaces. This methodology demonstrates the existence of fixed points for both single- and multi-valued mappings within complete vector-valued metric spaces. Through the utilization of binary relations and θ -contraction, this study advances and refines the Perov-type fixed-point results in the literature. Furthermore, this article furnishes examples to substantiate the validity of the presented results. Additionally, we establish an application for finding the existence of solutions to a system of matrix equations. [ABSTRACT FROM AUTHOR]

In this paper, we mainly explore the averaging principle of Caputo-type fractional delay stochastic differential equations with Brownian motion. Firstly, the solutions of this considered system are derived with the aid of the Picard iteration technique along with the Laplace transformation and its inverse. Secondly, we obtain the unique result by using the contradiction method. In addition, the averaging principle is discussed by means of the Burkholder-Davis-Gundy inequality, Jensen inequality, Hölder inequality and Grönwall-Bellman inequality under some hypotheses. Finally, an example with numerical simulations is carried out to prove the relevant theories. [ABSTRACT FROM AUTHOR]

In this paper, we focus on the nonlinear least squares problem: \min _{{\boldsymbol {x}}\in \mathbb {H}^d}\|\lvert A{\boldsymbol {x}}\rvert -{\boldsymbol {b}}\| where A\in \mathbb {H}^{m\times d}, {\boldsymbol {b}}\in \mathbb {R}^m with \mathbb {H}\in \left \{\mathbb {R},\mathbb {C}\right \} and consider the uniqueness and stability of solutions. This problem arises in applications such as phase retrieval and absolute value rectification neural networks. While several results have been developed to characterize the uniqueness and stability of solutions when {\boldsymbol {b}}=\lvert A{\boldsymbol {x}}_0\rvert for some {\boldsymbol {x}}_0\in \mathbb {H}^d, no existing results address the case where {\boldsymbol {b}} is arbitrary. In this paper, we investigate the uniqueness and stability of solutions for the more general case where {\boldsymbol {b}} is not necessarily equal to \lvert A{\boldsymbol {x}}_0\rvert for any {\boldsymbol {x}}_0\in \mathbb {H}^d. We prove that for any matrix A\in \mathbb {H}^{m\times d}, there is always a vector {\boldsymbol {b}}\in \mathbb {R}^m for which the solution to the nonlinear least squares problem is not unique. However, we show that such "bad" vectors {\boldsymbol {b}} are negligible in practice; specifically, if {\boldsymbol {b}}\in \mathbb {R}_{ }^m does not lie in some measure zero set, then the solution is unique. Furthermore, we establish certain conditions under which the solution is guaranteed to be unique. Regarding the stability of solutions, we prove that the solution is not uniformly stable. However, if we restrict the vectors {\boldsymbol {b}} to a convex set where the solution to the least squares problem is unique, then the solution becomes stable. To the best of our knowledge, our results represent the first theoretical results of the uniqueness and stability of solutions for the nonlinear least squares problem. [ABSTRACT FROM AUTHOR]

We consider a nonlinear coefficient inverse problem of reconstructing the density and the memory matrix of a viscoelastic medium by probing the medium with a family of wave fields excited by moment tensor point sources. A spatially non-overdetermined formulation is investigated, in which the manifolds of point sources and detectors do not coincide and have a total dimension equal to three. The requirements for these manifolds are established to ensure the unique solvability of the studied inverse problem. The results are achieved by reducing the problem to a chain of connected systems of linear integral equations of the M. M. Lavrentiev type. [ABSTRACT FROM AUTHOR]

The aim of this study is to analyze and investigate the COVID-19 transmission with effect of symptomatic and asymptomatic in the community. Mathematical model is converted into fractional order with the help of fractal fractional definition. The proposed fractional order system is investigated qualitatively as well as quantitatively to identify its stable position. Local stability of the COVID-19 system is verified and test the system is tested with flip bifurcation. Also the system is investigated for global stability using Lyapunov first and second derivative functions to see its rate of spread after recovery. The existence, boundedness and positivity of the COVID-19 are checked which are the key properties for such of type of epidemic problem to identify reliable findings. Effect of global derivative is demonstrated to verify its rate of effects according to their sub compartments to identify in which rate the symptomatic and asymptomatic transmission occurs. Solutions for fractional order system are derived with the help of advanced tool fractal fractional operator with generalized mittag-leffler kernel for different fractional values. Simulations are carried out to see symptomatic as well as asymptomatic effects of COVID-19 in the worldwide using MATLAB Coding. They show the actual behavior of COVID-19 especially for asymptomatic measures which will be helpful in early detection, also which will be helpful to understand the outbreak of COVID-19 as well as for future prediction and better control strategies. [ABSTRACT FROM AUTHOR]

In this paper, we consider a non-homogeneous generalized Kortewegde Vries problem with some hypotheses on the right-hand side, and we give a new regularity result of the solution in an anisotropic Sobolev space. Then we apply the obtained result to a non-homogeneous KdV problem. This work is an extension of solvability results for a right-hand side f in Lebesgue space. [ABSTRACT FROM AUTHOR]

The second-order mean field games system (MFGS) in a bounded domain with the lateral Cauchy data are considered. This means that both Dirichlet and Neumann boundary data for the solution of the MFGS are given. Two Hölder stability estimates for two slightly different cases are derived. These estimates indicate how stable the solution of the MFGS is with respect to the possible noise in the lateral Cauchy data. Our stability estimates imply uniqueness. The key mathematical apparatus is the apparatus of two new Carleman estimates. [ABSTRACT FROM AUTHOR]

The social life, economic issues, and health issues resulting from various diseases will be impacted by the use of the epidemiological model to address the negative effects of drinking in society. The paper aims to investigate a nonlinear drinking epidemic fractional SHTR model in the sense of a Constant Proportional Caputo (CPC) operator. For the CPC operator, a stability study of the fractional order model and the presence of a solution have been made. A nonlinear system of the suggested system has an approximative solution provided by the Laplace Adomian Decomposition technique. A convergence analysis of the system is also treated to show the effect and efficiency of the scheme. Additionally, we offer some numerical outcomes to demonstrate the efficiency of this operator. A comparative study for different values of α shows that these methods are effective for giving better results in fractional order as compared to classical order derivatives. [ABSTRACT FROM AUTHOR]

The global existence of mass‐conserving weak solutions to the Safronov–Dubovskiǐ coagulation equation is shown for the coagulation kernels satisfying at most linear growth for large sizes. In contrast to previous works, the proof mainly relies on the de la Vallée–Poussin theorem, which only requires the finiteness of the first moment of the initial condition. By showing the necessary regularity of solutions, it is shown that the weak solutions constructed herein are indeed classical solutions. Under additional restrictions on the initial data, the uniqueness of solutions is also shown. Finally, the continuous dependence on the initial data and the large‐time behavior of solutions are also addressed. [ABSTRACT FROM AUTHOR]

The aim of the paper is to study a new class of coupled variational–hemivariational inequalities with unilateral constraints and history‐dependent operators. First, by employing a fixed‐point theorem for history‐dependent operators combined with surjectivity theorem, we establish the existence and uniqueness of solution for coupled system. Second, we obtain a convergence result, namely, related penalized problems of solutions converge to the solution to the original system. Finally, we conclude with a new contact problem of the body pressure of two elastic materials. [ABSTRACT FROM AUTHOR]

We demonstrate that a convex combination of the Nagumo and Perron growth conditions guarantees the existence of a unique solution to an ordinary differential equation, which can be obtained as the uniform limit of a sequence of successive approximations. Furthermore, we give a sufficient condition for the pathwise uniqueness of solutions to stochastic differential equations driven by Brownian motions. [ABSTRACT FROM AUTHOR]

In this paper, we study the uniqueness of the steady 1-D shock solutions for the inviscid compressible Euler system in a finite nozzle via asymptotic analysis for physical parameters. The parameters for the heat conductivity and the temperature-depending viscosity are investigated for both barotropic gases and polytropic gases. It finally turns out that the hypotheses on the physical effects have significant influences on the asymptotic behaviors as the parameters vanish. In particular, the positions of the shock front for the limit shock solution (if exists) are different for different hypotheses. Hence, it seems impossible to figure out a criterion selecting the unique shock solution within the framework of the inviscid Euler flows. [ABSTRACT FROM AUTHOR]

In the paper, an inverse source problem in bioluminescence tomography (BLT) is investigated. BLT is a method of light imaging and offers many advantages such as sensitivity, cost-effectiveness, high signal-to-noise ratio and non-destructivity. It thus has promising prospects for many applications such as cancer diagnosis, drug discovery and development as well as gene therapies. In the literature, BLT is extensively studied based on the (stationary) diffusion approximation (DA) equation, where the distribution of peak sources is reconstructed and no solution uniqueness is guaranteed without proper a priori information. In this work, motivated by solution uniqueness, a novel dynamic coupled DA model is proposed. Theoretical analysis including the well-posedness of the forward problem and the solution uniqueness of the inverse problem are given. Based on the new model, iterative inversion algorithms under the framework of regularizing schemes are introduced and applied to reconstruct the smooth and non-smooth sources. We discretize the regularization functional with the finite element method and give the convergence rate of numerical solutions. Several numerical examples are implemented to validate the effectiveness of the new model and the proposed algorithms. [ABSTRACT FROM AUTHOR]

This paper is devoted to some inverse problems of recovering the nonlinearity for the Jordan–Moore–Gibson–Thompson equation, which is a third order nonlinear acoustic equation. This equation arises, for example, from the wave propagation in viscous thermally relaxing fluids. The well-posedness of the nonlinear equation is obtained with the small initial and boundary data. By the second order linearization to the nonlinear equation, and construction of complex geometric optics solutions for the linearized equation, the uniqueness of recovering the nonlinearity is derived. [ABSTRACT FROM AUTHOR]

Neutrosophic set is a generalization of classical sets, fuzzy set, intuitionistic sets etc. A mathematical notion neutrosophic set dealing issues containing inconsistent, indeterminate and imprecise data. In this manuscript, we toss the notion of Neutrosophic b-metric-like spaces and obtain some fixed point results in the sense of Neutrosophic b-metric-like spaces. Our results are improvements of recent results in the existing literature. For the validity of these results some non-trivial examples are imparted. [ABSTRACT FROM AUTHOR]

This paper delves into the numerical analysis of the extended Fisher-Kolmogorov (EFK) equation within open bounded convex domains R ⊂ R d , where d ≤ 3. Two distinct finite element schemes are introduced, namely the semi-discrete and fully-discrete finite element approximations. The existence and uniqueness of solutions are established for both the semi-discrete and fully-discrete finite element approximations. Error bounds are investigated across different scenarios, including comparisons between the semi-discrete and exact solutions, as well as between the semi-discrete and fully-discrete solutions, along with the fully-discrete and exact solutions. An effective algorithm has been proposed to solve the nonlinear system resulting from the fully-discrete finite element approximation at each time step. The paper also provides computed numerical error results and showcases a variety of numerical experiments to further illustrate and support the findings. [ABSTRACT FROM AUTHOR]

The extended cubic Camassa-Holm equation can be derived as asymptotic model from shallow-water approximation to the 2D incompressible Euler equations. This model encompasses both quadratic and cubic nonlinearities and the solution of the extended cubic Camassa-Holm equation possible development of singularities in finite time. This paper is devoted to the continuation of solutions to the extended cubic Camassa-Holm equation beyond wave breaking, and the global existence and uniqueness of the Hölder continuous energy conservative solutions for the Cauchy problem of the extended cubic Camassa-Holm type equation are investigated. An equivalent semilinear system was first introduced by a new set of independent and dependent variables, which can resolve all singularities due to possible wave breaking. Returning to the original variables, depending continuously on the initial data, the existence of the global conservative weak solutions can be obtained. Moreover, by analyzing the evolution of the quantities u and v = 2 arctan ⁡ u x along each characteristic, the uniqueness of the global conservative solutions for the Cauchy problem with general initial data u 0 ∈ H 1 (R) was proved. [ABSTRACT FROM AUTHOR]

This paper presents the computational analysis of fractional differential equations of variable‐order delay systems. To the proposed problem, the existence of solutions is derived using Arzela‐Ascoli theorem, and the Banach fixed point theorem is used for uniqueness results. To investigate and address the computational solutions, Adams‐Bashforth‐Moulton technique is established. To demonstrate the method's efficiency, computational simulations of chaotic behaviors in several one‐dimensional delayed systems with distinct variable orders are employed. The numerical solution of the proposed problem gives high precision approximations. [ABSTRACT FROM AUTHOR]

In this paper, we study the uniqueness of nodal radial solutions to nonlinear elliptic equations in the unit ball in ℝ3$$ {\mathrm{\mathbb{R}}}&#x0005E;3 $$. Under suitable conditions, we prove that, for any given positive integer k$$ k $$, the problem we considered has at most one solution possessing exactly k−1$$ k-1 $$ nodes. Together with the results presented by Nagasaki [J. Fac. Sci. Univ.  Tokyo Sect. IA Math. 36 (2): 211–232, 1989] and Tanaka [Proc. Roy. Soc. Edinburgh Sect. A. 138 (6): 1331–1343, 2008], we can prove that more types of nonlinear elliptic equations have the uniqueness of nodal radial solutions. [ABSTRACT FROM AUTHOR]

In this paper, we provide existence and uniqueness results for the initial value problems associated with mixed Riemann–Liouville/Caputo differential equations in the real domain. We show that, under appropriate conditions in a fractional order, solutions are always square-integrable on the finite interval under consideration. The results are valid for equations that have sign-indefinite leading terms and measurable coefficients. Existence and uniqueness theorem results are also provided for two-point boundary value problems in a closed interval. [ABSTRACT FROM AUTHOR]

Kim and Markus (1999; Study 3) found that 74% of European Americans selected a pen with an uncommon (vs. common) color, whereas only 24% of East Asians made such a choice, highlighting a pronounced cross-cultural difference in the extent to which people opt for originality or make majority-based choices. The present high-powered study (N = 729) conceptually replicates the results from Kim and Markus (1999; Study 3), although our effect size (r =.12) is significantly weaker than that of the original study (r =.52). Interestingly, a larger proportion of Chinese, but not US, participants selected a pen with an uncommon color now than during the original study. Thus, our findings indicate a potential transmission of certain Western values to cultures traditionally characterized by collectivism and conformity, likely exacerbated by the globalization of mass media and the rapid economic growth in many East Asian countries. [ABSTRACT FROM AUTHOR]

Extending an argument by Shatah and Struwe [Int. Math. Res. Not. 11 (2002), pp. 555–571] we obtain uniqueness for solutions of the half-wave map equation in dimension d \geq 3 in the natural energy class. [ABSTRACT FROM AUTHOR]

The goal of this study is to describe the class of modified Sehgal–Guseman-like contraction mappings and set up some fixed-point results in S -metric spaces. The class of generalized Sehgal–Guseman-like contraction mappings contains enhancements of Banach contractions, Kannan contractions, Chatterjee contractions, Chatterjee-type contractions, quasi-contractions, Ćirić–Reich–Rus-type contractions, Hardy–Rogers-type contractions, Reich-type contractions, interpolative Kannan contractions, interpolative Chatterjee contractions, among others, with their generalizations in S -metric spaces. We offer significant examples to substantiate the reliability of our results. This study also establishes consequential fixed-point results and applies them to nonlinear fractional differential equations and the boundary value problem for homogeneous transverse bars. At the end of the manuscript, we present an important open problem. [ABSTRACT FROM AUTHOR]

We study the incompressible stationary Navier-Stokes equations in the upper-half plane with homogeneous Dirichlet boundary condition and non-zero external forcing terms. Existence of weak solutions is proved under a suitable condition on the external forces. Weak-strong uniqueness criteria based on various growth conditions at the infinity of weak solutions are also given. This is done by employing an energy estimate and a Hardy's inequality. Several estimates of stream functions are carried out and two density lemmas with suitable weights for the homogeneous Sobolev space on 2-dimensional space are proved. [ABSTRACT FROM AUTHOR]

The well-posedness of an initial–boundary value problem for a model parabolic equation with two power-law degeneration lines is studied. Two initial–boundary value problems depending on the degeneracy exponents are stated, and uniqueness and existence theorems are proved. The solutions of these problems are constructed in closed form. [ABSTRACT FROM AUTHOR]

We study the incompressible stationary Navier-Stokes equations in the upper-half plane with homogeneous Dirichlet boundary condition and non-zero external forcing terms. Existence of weak solutions is proved under a suitable condition on the external forces. Weak-strong uniqueness criteria based on various growth conditions at the infinity of weak solutions are also given. This is done by employing an energy estimate and a Hardy's inequality. Several estimates of stream functions are carried out and two density lemmas with suitable weights for the homogeneous Sobolev space on 2-dimensional space are proved. [ABSTRACT FROM AUTHOR]

This article establishes the existence of global classical solutions to discrete coagulation equations with collisional breakage for collision kernels having linear growth. In contrast, the uniqueness is shown under additional restrictions on collision kernels. Moreover, mass conservation property and the positivity of solutions are also shown. While coagulation dominates, the occurrence of the gelation phenomenon for kernels having specific growth is also studied. [ABSTRACT FROM AUTHOR]

This study aims to prove the existence and uniqueness of the (ω , c) -periodic solution as a specific solution to Hadamard impulsive boundary value integro-differential equations with fixed lower limits. The results are proven using the Banach contraction, Schaefer's fixed point theorem, and the Arzelà–Ascoli theorem. Furthermore, we establish the necessary conditions for a set of solutions to the explored boundary values with impulsive fractional differentials. Finally, we present two examples as applications for our results. [ABSTRACT FROM AUTHOR]

Over 750 native bird species reside in or regularly migrate to Australia, many of which have experienced rapid changes in habitat extent over the past two centuries. By 2020, eight taxa were considered Extinct and 10% threatened with extinction. Understanding the underlying extrinsic and intrinsic factors that increase extinction risk can allow prioritisation of conservation management and research. Here, we use state-of-the-art phylogenetic comparative models to reveal the most important biological traits that predispose Australian bird species to elevated extinction risk. We use an extensive database of their biological traits and relate these to each species' national and global IUCN extinction risk status as assessed over the past three decades (in 1990, 2000, 2010, and 2020). We show that high evolutionary distinctiveness (uniqueness), island endemism, and an inability to take advantage of agricultural habitats were the most important traits explaining elevated extinction risk in species when phylogeny is controlled for, suggesting that extinction risk is disproportionately high in species with high evolutionary distinctiveness. Extinct taxa were characterised by large body mass and island endemism compared to taxa extant in 2020. Our study provides the largest and most up-to-date analysis of the intrinsic traits of Australian birds in relation to their extinction risk, and can be used as a baseline in future studies, for prioritisation of conservation actions, and for policy advice on a broad scale. Phylogenetic analyses are a useful tool for anticipating extinction risk. Extinction risk over the past three decades is highest among species with a high level of evolutionary distinctiveness. Species-level assessments can mask higher extinction risk at the subspecies-level. Conservation actions that reduce extinction risk can influence the variables deemed important in predictive models. [ABSTRACT FROM AUTHOR]

We study the solvability of the Ionkin problem for some differential equations with one space variable. These equations include parabolic and quasiparabolic, hyperbolic and quasihyperbolic, pseudoparabolic and pseudohyperbolic, elliptic and quasielliptic equations and equations of many other types. For the above equations, the following theorems are proved with the use of the splitting method: the existence of regular solutions—solutions that all have weak derivatives in the sense of S. L. Sobolev and occur in the corresponding equation. [ABSTRACT FROM AUTHOR]

In this paper, we prove an existence and uniqueness result for a class of Dirichlet boundary value problems whose model is − Δ p u = β | ∇ u | q + c | u | p − 2 u + f in   Ω , u = 0 on   ∂ Ω , where Ω is an open bounded subset of R N , N ≥ 2 , 1 < p < N , Δ p u is the so-called p-Laplace operator, and p − 1 < q < p . We assume that β is a positive constant, c and f are measurable functions belonging to suitable Lorentz spaces. Our approach is based on Schauder fixed point theorem. [ABSTRACT FROM AUTHOR]

We investigate the uniqueness problems of meromorphic functions and their difference operators by using a new method. It is proved that if a non-constant meromorphic function f shares a non-zero constant and ∞ counting multiplicities with its difference operators Δcf(z) and Δ c 2 f (z) , then Δ c f (z) ≡ Δ c 2 f (z) . In particular, we give a difference analogue of a result of Jank–Mues–Volkmann. Our method has two distinct features: (i) It converts the relations between functions into the corresponding vectors. This makes it possible to deal with the uniqueness problem by linear algebra and combinatorics. (ii) It circumvents the obstacle of the difference logarithmic derivative lemma for meromorphic functions of infinite order, since this method does not depend on the growth of the functions. Furthermore, the idea in this paper can also be applied to the case for several variables. [ABSTRACT FROM AUTHOR]

In this paper we consider the three-phase-lag model of heat conduction that involves second-order effects in phase lag of the heat flux vector. This model leads to a fourth-order in time equation of Moore–Gibson–Thompson type. We use the thermodynamic restrictions derived from the compatibility of the constitutive equation with the Second Law of Thermodynamics to study the properties of the solutions of the initial boundary value problems associated with the model in concern. In this connection we establish a series of well-posedness results concerning the related solutions like: uniqueness, continuous data dependence, exponentially stability or domain of influence. Furthermore, based on the thermodynamic restrictions, we show that the thermal model in question admits damped in time propagating waves as well as exponentially decaying standing modes. We also show that when the thermodynamic restrictions are not fulfilled, then wave solutions appear that cause the energy blows up as time goes to infinity. [ABSTRACT FROM AUTHOR]

In this paper, we consider the existence and uniqueness of mild solutions for stochastic nonlocal evolution equations with Lévy diffusion operator and nonlocal initial conditions. Based on the continuity of the Lévy semigroup and the technique of the measure of noncompactness, we establish the local existence of mild solutions in C 0 , T ; L q (Ω ; L q (ℝ N)) under some weaker growth conditions. Moreover, we obtain the existence of mild solutions on any finite interval by using the general growth conditions on the nonlinear. Finally, the global existence and uniqueness of mild solutions follow from the additional Lipschitz conditions on nonlinear terms. [ABSTRACT FROM AUTHOR]

This article establishes the existence of global classical solutions to discrete coagulation equations with collisional breakage for collision kernels having linear growth. In contrast, the uniqueness is shown under additional restrictions on collision kernels. Moreover, mass conservation property and the positivity of solutions are also shown. While coagulation dominates, the occurrence of the gelation phenomenon for kernels having specific growth is also studied. [ABSTRACT FROM AUTHOR]

This article concerns the uniqueness of an inverse problem of simultaneously identifying the space‐dependent coefficient and source in a one‐dimensional time‐fractional diffusion equation with derivative order α∈(0,1)$$ \alpha \in \left(0,1\right) $$ and the zero Neumann boundary value. By additional boundary measurements, we first obtain the uniqueness of the coefficient from the Laplace transform and a transformation formula. Then, we further show the uniqueness of the source through the asymptotic behavior of solutions to the corresponding forward problem. The result shows that the uniqueness of the simultaneous identification can be obtained under the condition that the prior information only on one set of parameters in the model is given other than that of two sets. [ABSTRACT FROM AUTHOR]

In this work, a new type of the unique continuation property for time-fractional diffusion equations is studied. The proof is mainly based on the Laplace transform and the properties of Bessel functions. As an application, the uniqueness of the inverse problem in the simultaneous determination of spatially dependent source terms and fractional order from sparse boundary observation data is established. [ABSTRACT FROM AUTHOR]