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This paper is concerned with the existence of an eigenvalue for a p(x)-biharmonic Kirchhoff problem with Navier boundary condition. Under some suitable conditions, we establish that any λ > 0 is an eigenvalue . The proofs combine variational methods with energy estimates. The main results of this paper improve and generalize the previous one introduced by Kefi and Radulescu (Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. 29 (2018), 439-463).

Moment functions play a basic role in probability theory. A natural generalization can be defined on hypergroups which leads to the concept of generalized moment function sequences. In a former paper we studied some function classes on hypergroup joins which play a basic role in spectral synthesis. Moment functions are also important basic blocks of spectral synthesis. All these functions can be characterized by well-known functional equations. In this paper we describe generalized moment function sequences on hypergroup joins.

In this paper, we discuss the existence of symmetric positive solutions for the systems of higher-order boundary value problems on time scales. Our results extend some recent work in the literature. The analysis of this paper mainly relies on the monotone iterative technique.

Main objective of the present paper is to prove solvability of the Dirichlet, Neumann and Mixed boundary value problems for an anisotropic Laplace-Beltrami equation on a hypersurface $$${C}$$$ with the Lipschitz boundary $$${\Gamma=∂C}$$$ in the classical $$${𝕎^1(C)}$$$ space setting.

An evolutionary game is usually identified by a smooth (possibly nonlinear) payoff function. In this paper, we propose a model of evolutionary game in which the nonlinear payoff functions are defined by the Ricker models. Namely, in the proposed model, the biological fitness of the pure strategy will increase according to the Ricker model. Motivated by some models of economics of transportation and communication networks, in order to observe the evolutionary bifurcation diagram, we also control the nonlinear payoff functions in two different regimes: positive and negative. One of the interesting feature of the model is that if we switch the controlling parameter from positive to negative regime then the set of local evolutionarily stable strategies (ESSs) changes from one set to another one. We also study the dynamics and stability analysis of the discrete-time replicator equation governed by the proposed nonlinear payoff function. In the long-run time, the following scenario can be observed: (i) in the positive regime, the active dominating pure strategies will outcompete other strategies and only they will survive forever; (ii) in the negative regime, all active pure strategies will coexist together and they will survive forever.

This paper is devoted to the study of the nonhomogeneous problem $$$ -div (a(|\nabla u|)\nabla u)+a(| u|)u=\lambda V(x)|u|^{m(x)-2}u-\mu g(x,u) \mbox{ in} \ \Omega, \ u=0 \mbox{ on} \ \partial\Omega ,$$$ where $$$\Omega$$$ is a bounded smooth domain in $$$\mathbb{R}^N,\lambda, \mu$$$ are positive real numbers, $$$V(x)$$$ is a potential, $$$ m: \overline{ \Omega} \to (1, \infty)$$$ is a continuous function, $$$a$$$ is mapping such that $$$ \varphi(|t|)t$$$ is increasing homeomorphism from ℝ to ℝ and $$$g: \overline{\Omega}\times ℝ \to ℝ$$$ is a continuous function. We establish there main results with various assumptions, the first one asserts that any $$$\lambda$$$0> is an eigenvalue of our problem. The second Theorem states the existence of a constant $$$\lambda^{*}$$$ such that every $$$\lambda \in (0,\lambda^{*})$$$ is an eigenvalue of the problem. While the third Theorem claims the existence of a constant $$$\lambda^{**}$$$ such that every $$$\lambda \in [\lambda^{**},\infty)$$$ is an eigenvalue of the problem. Our approach relies on adequate variational methods in Orlicz-Sobolev spaces.

In this paper, we consider the following inhomogeneous nonlinear Schrodinger equation (INLS) $$$i\partial_t u + \Delta u + \mu$$$ |$$$x$$$|$$$^{-b}$$$|$$$u$$$|$$$^\alpha u = 0, \quad (t,x)\in ℝ \times ℝ^d$$$ with $$$b, \alpha$$$ > 0. First, we revisit the local well-posedness in $$$H^1(ℝ^d)$$$ for (INLS) of Guzman [Nonlinear Anal. Real World Appl. 37 (2017), 249-286] and give an improvement of this result in the two and three spatial dimensional cases. Second, we study the decay of global solutions for the defocusing (INLS), i.e. $$$\mu=-1$$$ when 0 < $$$\alpha$$$ < $$$\alpha^\star$$$ where $$$\alpha^\star = \frac{4-2b}{d-2}$$$ for $$$d\geq 3$$$, and $$$\alpha^\star = \infty$$$ for $$$d=1, 2$$$ by assuming that the initial data belongs to the weighted $$$L^2$$$ space $$$\Sigma =\{u \in H^1(ℝ^d) :$$$ |$$$x$$$|$$$ u \in L^2(ℝ^d) \}$$$. Finally, we combine the local theory and the decaying property to show the scattering in $$$\Sigma$$$ for the defocusing (INLS) in the case $$$\alpha_\star$$$ < $$$\alpha$$$ < $$$\alpha^\star$$$, where $$$\alpha_\star = \frac{4-2b}{d}$$$.

The aim of this paper is to construct invariant regions of a generalized m-component reaction-diffusion system with tridiagonal symmetric Toeplitz diffusion matrix and nonhomogeneous boundary conditions and polynomial growth for the nonlinear reaction terms. Using the eigenvalues and eigenvectors of the diffusion matrix and the parabolicity conditions. So we prove the global existence of solutions using Lyapunov functional.

In this paper, we are interested in the study of the existence of positive solutions for the following nonlinear boundary value problem on the half-line:\left\{\begin{aligned} \displaystyle-u^{\prime\prime}(x)&\displaystyle=q(x)f(x% ,u,u^{\prime}),&&\displaystyle x\in(0,+\infty),\\ \displaystyle u^{\prime}(0)&\displaystyle=u^{\prime}(+\infty)=0,\end{aligned}\right.where {q:\mathbb{R^{+}}\rightarrow\mathbb{R^{+}}} is a positive measurable function such that {\int_{0}^{+\infty}q(x)\,dx=1} and {f:\mathbb{R}^{+}\times\mathbb{R}^{2}\rightarrow\mathbb{R}} is q-Carathéodory.

In this paper, we investigate the deterministic and stochastic prey-predator system with refuge. The basic local stability results for the deterministic model have been performed. It is found that all the equilibrium points except the positive coexisting equilibrium point of the deterministic model are independent of the prey refuge. The trivial equilibrium point, predator free equilibrium point and prey free equilibrium point are always unstable (saddle point). The existence and local stability of the coexisting equilibrium point is related to the prey refuge. The permanence and extinction conditions of the proposed biological model have been studied rigourously. It is observed that the stochastic effect may be seen in the form of decaying of the species. The numerical simulations for different values of the refuge values have also been included for understanding the behavior of the model graphically.

A non-trivial multi-norm structure based on the enveloping {C^{*}}-algebras will be discussed in this paper. The main example is group {C^{*}}-algebras on compact groups. Also a (generalizing) non-trivial multi-norm structure based on the Fourier and Fourier–Stieltjes algebras on compact groups will be given.

In this paper, we introduce an iterative scheme involving an inertial term and a step size independent of the operator norm for approximating a solution to a split variational inequality problem in a real Hilbert space. Furthermore, we prove a convergence theorem for the sequence generated by the proposed operator norm independent inertial accelerated iterative scheme. We applied our result to solve split convex minimization problems, split zero problem and further give a numerical example to demonstrate the efficiency of the proposed algorithm.

In this paper, we consider a Brück-type result for a homogeneous differential polynomial generated by a meromorphic function.

In this paper, we consider the Cauchy problem for the relativistic Enskog equation with near vacuum data for a hard sphere gas in the Robertson–Walker space-time. We prove an existence and uniqueness result of the global (in time) mild solution in a suitable weighted space. We also study the asymptotic behavior of the solution as well as the {L^{\infty}} -stability.

In this paper, we prove two theorems establishing the uniqueness of the derivatives of meromorphic functions{f^{{(k)}\vphantom{k}}}and{g^{{(k)}\vphantom{k}}}when they share two sets with least cardinalities. Our results improve some existing results of Fang–Lahiri, Banerjee–Bhattacharjee, Banerjee–Mallick and Banerjee–Chakraborty.

Let {(X,*)} be a hypergroup and let {w_{0}} be a fixed measure on X. In this paper we study the two functional equations \langle\delta_{x}*\delta_{y}*\omega_{0},g\rangle+\langle\delta_{x}*\delta_{% \check{y}}*\omega_{0},g\rangle=2g(x)g(y),\quad x,y\in X, and \langle\delta_{x}*\delta_{\check{y}}*\omega_{0},f\rangle-\langle\delta_{x}*% \delta_{y}*\omega_{0},f\rangle=2f(x)f(y),\quad x,y\in X, where {g,f:X\to\mathbb{C}} are continuous and bounded functions to be determined. We express the solutions of the two functional equations in terms of multiplicative maps on {(X,*)} . As an application we give the solution of the two functional equations on polynomial and Sturm–Liouville hypergroups.

In this paper, we study well-posedness, existence of a lower finite time blow-up bound and variants of controllability of the classical chemotaxis model in {\Omega\times(0,T)} , where {\Omega\subset\mathbb{R}^{N}} , {N=1,2,3} . The spatial domain restrictions allow the system with initial data in {L^{2}(\Omega)} to admit a solution in L^{\infty}[0,T;L^{2}(\Omega))\cap L^{2}(0,T;H^{1}(\Omega)) and to have the property that the gradient chemical solutions are uniformly bounded in {\Omega\times(0,T)} . A lower finite time blow-up bound of solutions in the norm of {L^{2}(\Omega)} is proved using the differential inequality technique. Furthermore, using Carleman estimates and appropriate energy functionals, we show that the model is null and approximate controllable at any finite time {T>0} with a single control in {L^{2}(\omega\times(0,T))} acting on the cell-density equation, linearized through a priori uniform boundedness of the chemical drift solutions, where {\omega\subset\Omega} is a non-empty open subset of Ω. Lastly, bang-bang-type controls for the problem are constructed.

In this paper, we consider the Timoshenko-type system with nonlinear boundary dissipation. We prove the existence and uniqueness of the solution and we establish an explicit and general decay result for a wide class of the relaxation function, which depends on the length of the beam.

In this paper, we present a new differential operator of arbitrary order defined by means of a Caputo-type modification of the generalized fractional derivative recently proposed by Katugampola. The generalized fractional derivative, when convenient limits are considered, recovers the Riemann–Liouville and the Hadamard derivatives of arbitrary order. Our differential operator recovers as limiting cases the arbitrary order derivatives proposed by Caputo and by Caputo–Hadamard. Some properties are presented as well as the relation between this differential operator of arbitrary order and the Katugampola generalized fractional operator. As an application we prove the fundamental theorem of fractional calculus associated with our operator.

In the present paper, it is shown that if a prime ring R admits a generalized derivation f associated with a nonzero derivation d such that either f([x^{m},y^{n}])+[x^{m},y^{n}]\in Z(R)\quad\text{for all }x,y\in R or f([x^{m},y^{n}])-[x^{m},y^{n}]\in Z(R)\quad\text{for all }x,y\in R, then R is commutative. We apply this purely ring theoretic result to obtain commutativity of Banach algebras and prove that if A is a prime Banach algebra which admits a continuous linear generalized derivation f associated with a nonzero continuous linear derivation d such that either {f([x^{m},y^{n}])-[x^{m},y^{n}]\in Z(A)} or {f([x^{m},y^{n}])+[x^{m},y^{n}]\in Z(A)} for an integer {m=m(x,y)>1} and sufficiently many {x,y} in A, then A is commutative. A similar result is obtained for a unital prime Banach algebra A which admits a nonzero continuous linear generalized derivation f associated with a continuous linear derivation d such that {d(Z(A))\neq 0} satisfying either {f((xy)^{m})-x^{m}y^{m}\in Z(A)} or {f((xy)^{m})-y^{m}x^{m}\in Z(A)} for each {x\in G_{1}} and {y\in G_{2}} , where {G_{1},G_{2}} are open sets in A and {m=m(x,y)>1} is an integer: then A is commutative.

In this article, we correct the proof of the main theorem of Gordji’s paper [M. Eshaghi Gordji, n-Jordan homomorphisms, Bull. Aust. Math. Soc. 80 2009, 1, 159–164] by a different method and generalize Zelazko’s theorem to 4-Jordan homomorphisms by considering an extra condition.

In this paper, we study varieties and characterize convolution operators on the algebras related to the new structures of KPC-hypergroups, which are a generalization of the classical ones.

In this paper, by employing a critical point theorem, we establish the existence of infinitely many solutions for fourth-order impulsive differential equations depending on two real parameters.

Alexandroff spaces are the topological spaces in which the intersection of arbitrary many open sets is open. Let T be an indecomposable tournament. In this paper, first, we associate a trivial topology to T. Then we define another topology on T, called the graphic topology of T, and we show that it is an Alexandroff topology. Our motivation is to investigate some properties of this topology.

Let G be a type 1 connected and simply connected solvable Lie group. The generalized moment map for π in {\widehat{G}} , the unitary dual of G, sends smooth vectors of the representation space of π to {{\mathcal{U}(\mathfrak{g})}^{*}} , the dual vector space of {\mathcal{U}(\mathfrak{g})} . The convex hull of the image of the generalized moment map for π is called its generalized moment set, denoted by {J(\pi)} . We say that {\widehat{G}} is generalized moment separable when the generalized moment sets differ for any pair of distinct irreducible unitary representations. Our main result in this paper provides a second proof of the generalized moment separability theorem for G.

The purpose of this paper is to study Ricci semisymmetric paracontact metric manifolds satisfying{\nabla_{\xi}h=0}and such that the sectional curvature of the plane section containing ξ equals a non-zero constantc. Also, we study paracontact metric manifolds satisfying the curvature condition{Q\cdot R=0}, whereQandRare the Ricci operator and the Riemannian curvature tensor, respectively, and second order symmetric parallel tensors in paracontact metric manifolds under the same conditions. Several consequences of these results are discussed.

In this paper, we propose an iterative algorithm for approximating a common fixed point of an infinite family of quasi-Bregman nonexpansive mappings which is also a solution to finite systems of convex minimization problems and variational inequality problems in real reflexive Banach spaces. We obtain a strong convergence result and give applications of our result to finding zeroes of an infinite family of Bregman inverse strongly monotone operators and a finite system of equilibrium problems in real reflexive Banach spaces. Our result extends many recent corresponding results in literature.

In this paper, we consider the system \left\{\begin{aligned} &\displaystyle{-}M_{1}\bigg{(}\int_{\Omega}\frac{\lvert% \nabla u\rvert^{p(x)}+\lvert u\rvert^{p(x)}}{p(x)}\,dx\biggr{)}(\Delta_{p(x)}u% -\lvert u\rvert^{p(x)-2}u)=\lambda a(x)\lvert u\rvert^{r_{1}(x)-2}u-\mu b(x)% \lvert u\rvert^{\alpha(x)-2}u&&\displaystyle\text{in }\Omega,\\ &\displaystyle{-}M_{2}\bigg{(}\int_{\Omega}\frac{\lvert\nabla v\rvert^{q(x)}+% \lvert v\rvert^{q(x)}}{q(x)}\,dx\biggr{)}(\Delta_{q(x)}v-\lvert v\rvert^{q(x)-% 2}v)=\lambda c(x)\lvert v\rvert^{r_{2}(x)-2}v-\mu d(x)\lvert v\rvert^{\beta(x)% -2}v&&\displaystyle\text{in }\Omega,\\ &\displaystyle u=v=0&&\displaystyle\text{on }\partial\Omega,\end{aligned}\right. where Ω is a bounded domain in {\mathbb{R}^{N}} ( {N\geq 2} ) with a smooth boundary {\partial\Omega} , {M_{1}(t),M_{2}(t)} are continuous functions and {\lambda,\mu>0} . We prove that for any {\mu>0} there exists {\lambda_{*}} sufficiently small such that for any {\lambda\in(0,\lambda_{*})} the above system has a nontrivial weak solution. The proof relies on some variational arguments based on Ekeland’s variational principle, and some adequate variational methods.

In this paper, we define various kinds of transitivity of maps onG-spaces. We obtain conditions onG-spaces and on maps for one type of transitivity to imply another type of transitivity. Giving several examples and proving various equivalences, we provide a complete description of the relationships among the different types of transitivities defined for maps onG-spaces.

The objective of the present paper is to develop a comprehensive theory of entropy in the realm of ags-space{(L,p)}involving the notion of a generalizeds-map, and to study dynamics of ap-preserving system{(L,p,\phi)}. It is obtained that the entropy ofp-preserving systems is isomorphism invariant, and also entropy of an invertiblep-preserving system vanishes provided the corresponding Rokhlin space admits a one-sided generator.

The object of the present paper is to study generalized Sasakian-space-forms satisfying the curvature condition{P(\xi,Y)\cdot W=0}. Moreover, ϕ-M-projectively semisymmetric and ϕ-pseudo-projectively semisymmetric generalized Sasakian-space-forms are also studied.

In this paper, first we introduce the categories of “n-ary hyperstructures” ({{\mathrm{HS}}_{n}}) and “n-ary hyperstructures with particular carriers and relations” ({{\mathrm{HSP}}_{n}}), and we prove that the categories of{{\mathrm{HS}}_{n}}and{{\mathrm{HSP}}_{n-1}}are isomorphic. Then we prove that the category of “{(n-1)}-ary hypergroupoids” ({{\mathrm{HG}}_{n-1}}) is a full subcategory of the category{{\mathrm{HS}}_{n}}and the category of “unary bindingn-ary algebra with particular properties” ({{\mathrm{UBA}}_{n}}) is a full subcategory of the category{{\mathrm{HSP}}_{n}}. Next, we define two functorsFandG, and show that the restriction of the functorFto the category{{\mathrm{HG}}_{n}}is an isomorphism of{{\mathrm{HG}}_{n}}onto{{\mathrm{UBA}}_{n}}, and the restriction of the functorGto the category{{\mathrm{UBA}}_{n}}is an isomorphism of{{\mathrm{UBA}}_{n}}onto{{\mathrm{HG}}_{n}}.

In this paper, it is shown that, if R is a ∗-ring containing a nontrivial self adjoint idempotent which admits a ∗-Lie higher derivable mapping L={Ln}n∈N, then there exists an element ZX,Y (depending on X and Y) in the center Z(R) such that Ln(X+Y)=Ln(X)+Ln(Y)+ZX,Y.

In this paper, using sub-supersolution argument, we prove some existence results on positive solution for a class of nonlocal elliptic systems with multiple parameters in bounded domains.

In this paper we shall find some sufficient conditions for a uniqueness polynomial to be a strong uniqueness polynomial, as this type of problem was never investigated by researchers earlier. We also exhibit some examples to substantiate our theorems.

Austin-Moore hemiarthroplasty had been critically utilized for aged patients with femoral neck fractures. However, this implant became no longer favorable when increasing life activity. A multiobjective shape optimization has been integrated to improve its performance. The resulting configuration is called Improved Austin-Moore (IAM) model. Probabilistic analysis is very important when the input data are random, that leads to stochastic results. In this paper, a probabilistic analysis is applied to solid and IAM stems implanted in a proximal femur in order to show their advantages. This way it is possible to control the biomechanical effects of the implanted femur to determine its performance. The applied loads are generated randomly using Monte Carlo Simulations (MCS). MSC sampling technique is applied and the different von-Mises stresses of the layers (bone and metal) are selected as performance indicators. Two simple 2D implant-bone models of the solid and IAM designs are studied with a target reliability index equals to  3 t , which corresponds to a high level of confidence (reliability) 99.87%. The major finding of this article is that the skewness values of all output parameters of the IAM stem are positive which means that the majority of the maximum von-Mises stress values are closer to their minimum values than those associated with the solid stem. In addition, the sensitivity analysis shows that the input parameters for the IAM stem are more effective on the output parameters relative to those associated with the solid stem. The IAM stem shows a high interdependence (correlation) between the input and output parameters when comparing with the solid stem. Since this study is carried out considering loading uncertainty, the geometry can affect the load transfer. Therefore, a correlation study between the input parameters is carried out and showed significant coefficient values for the IAM stem relative to the solid one. The results show that the IAM stem is much more advantageous than the solid stem.

Computational Fluid Dynamics (CFD) incorporates mathematical relations and algorithms to analyze and solve the problems regarding fluid flow. CFD analysis of an airfoil produces results such as lift and drag forces which determines the ability of an airfoil. In this paper a transonic flow will be modelled over a NACA 0012 airfoil for which experimental data has been published, so that a comparison can be made. The flow to be considered is compressible and turbulent and the solver used is the density based implicit solver, which gives good results for high speed compressible flows. The results show that the predicted lift, drag and pressure coefficients are in good agreement with experimental data.

In engineering, under complex nonlinear constraints, the majority of design problems are generally multiobjective. For multi-objective problems, the computing effort can often rise significantly through the number of objectives and constraints evaluations. Metaheuristics are nowadays seen as powerful algorithms to deal with multiobjective optimization problems. In this paper, we using Backtracking Search Algorithm (BSA) as a tool to solve multiobjective optimization problems in structures, named (BSAMO). A well known benchmark multi-objective problem has been chosen from the literature to demonstrate the validity of the proposed method, applicability of the method for structural problems has been tested through a truss problem and promising results were obtained. The numerical results show not only the effectiveness and the best performance of BSAMO compared to NSGA-II, but also its rapidity and efficiency.

In this paper, we study a transmission problem given by a system of two nonlinear equations of

In this paper, based on the mountain pass theorem and Ekeland’s variational principle, we show the existence of solutions for a class of non-homogeneous and nonlocal problems in Orlicz–Sobolev spaces.

In this paper, some new sufficient conditions are established for the oscillation of all solutions of the second-order neutral differential equation with mixed neutral terms of the formfor all

The objective of the present paper is to study some new results on quasi-conformal curvature tensor in a Kenmotsu manifold with respect to a semi-symmetric non-metric connection.

The purpose of the paper is to study uniqueness problems of certain types of differential-difference polynomials sharing a nonzero polynomial of certain degree under relaxed sharing hypotheses. We not only point out some gaps in the proof of the main results in [

The main goal of this paper is to give potential theoretical approach to study the Dunkl Laplacian $\Delta_k$ which is a standard example of differential-difference operators. By introducing the Green kernel relative to $\Delta_k$, we prove that the Dunkl Laplacian generates a balayage space and we investigate the associated family of harmonic measures. Therefore, by mean of harmonic kernels, we give a characterization of all $\Delta_k$-harmonic functions on large class of open subsets $U$ of $\mathbb{R}^d$. We also establish existence and uniqueness result of a solution of the corresponding Dirichlet problem., Comment: 21 pages

In this paper, we introduce the notion of an energy graph

In a previous paper we introduced a family of differential-reflection operators

In this paper, new inequalities connected with the celebrated Steffensen’s integral inequality are proved.

In this paper, using a generalized translation operator, we obtain an analog of Younis’ theorem, [

In this paper, we give necessary and sufficient conditions for a homogeneous cone Ω to be symmetric in two ways. One is by using the multiplier matrix of Ω, and the other is in terms of the basic relative invariants of Ω. In the latter approach, we need to show that the real parts of certain meromorphic rational functions obtained by the basic relative invariants are always positive on the tube domains over Ω. This is a generalization of a result of Ishi and Nomura [Math. Z. 259 (2008), 604–674].

This paper proposes an iterative method for solving an operator equation on a separable Hilbert space