HAL is a multi-disciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers. L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau...

The paper deals with the existence and uniqueness of a non-trivial solution to non-homogeneous p(x)- Laplacian equations, managed by non polynomial growth operator in framework variable exponent Sobolev spaces on Riemannian manifolds. mountain pass Theorem is used.

We will show how to use the mountain pass theorem to obtain nontrivial solutions of a certain two point BVP for the 2nth order, n ∈ N (formally) self-adjoint nonlinear difference equation n ∑ i=0 [ri(t) u(t − i)] = f (t, u(t)), t ∈ [a, b]Z. No periodicity assumptions will be placed on ri, i = 0, 1, . . . , n or f and it will be assumed that f grows superlinearly both at the origin and at infini...

We consider P 0 nonlinear complementarity problems and study the con-nectedness and stability of the solutions by applying degree theory and the Mountain Pass Theorem to a smooth reformulation of the complementarity problem. We show that the solution set is connected and bounded if a bounded isolated component of the solution set exists and that a solution is locally unique if and only if it is...

The aim of this paper is to establish the existence at least two non-zero homoclinic solutions for a nonlinear Laplacian difference equation without using Ambrosetti-Rabinowitz type-conditions. main tools are mountain pass theorem and Palais-Smale compactness condition involving suitable functionals.

Let G = (V, E) be a locally finite graph, Ω ⊂ V be a bounded open domain, ∆ be the usual graph Laplacian, and λ1(Ω) be the first eigenvalue of −∆ with respect to Dirichlet boundary condition. Using the mountain pass theorem of Ambrosette and Rabinowitz, We prove that if α < λ1(Ω), then for any p > 2, there exists a positive solution to  −∆u − αu = |u| p−2u in Ω◦, u = 0 on ∂Ω, where Ω◦ and...

This article concerns the nonhomogeneous Klein-Gordon-Maxwell equation −∆u+ u− (2ω + φ)φu = |u|p−1u+ h(x), in R, ∆φ = (ω + φ)u, in R, where ω > 0 is constant, p ∈ (1, 5). Under appropriate assumptions on h(x), the existence of at least two solutions is obtained by applying the Ekeland’s variational principle and the Mountain Pass Theorem in critical point theory.

We study the existence of non-trivial solutions for a class of problems containing in particular the following system of two coupled semilinear Poisson equations: (I) 8 > < > : ? v = f(u) in ; ? u = g(v) in ; u = v = 0 on @: (1) (2) (3) Here is a bounded domain in R N with a smooth boundary, and is the Laplace operator. Problem (I) allows for a variational formulation, i.e. solutions arise as c...

orography plays a substantial role in the formation and evolution of many atmospheric phenomena. observations indicate that two mountain ranges to the southwest of the red sea and west of iran (zagross mountain range) play a crucial role in the formation, evolution and activities of synoptic weather systems over iran. observations also, indicate that there are considerable differences between t...

The existence, nonexistence and multiplicity of positive radially symmetric solutions to a class of Schrödinger–Poisson type systems with critical nonlocal term are studied with variational methods. The existence of both the ground state solution and mountain pass type solutions are proved. It is shown that the parameter ranges of existence and nonexistence of positive solutions for the critica...