We prove a saddle point theorem for locally Lipschitz functionals with arguments based on a version of the mountain pass theorem for such kind of functionals. This abstract result is applied to solve two diierent types of multivalued semilinear elliptic boundary value problems with a Laplace{Beltrami operator on a smooth compact Riemannian manifold. The mountain pass theorem of Ambrosetti and R...

In this article, we consider the multiplicity of solutions for nonhomogeneous Schrodinger-Poisson systems under Berestycki-Lions type conditions. With aid Ekeland's variational principle, mountain pass theorem and a Pohozaev identity, prove that system has at least two positive solutions.
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A minimax variational method for finding mountain pass-type solutions with prescribed energy levels is introduced. The based on application of the Linking Theorem to energy-level nonlinear Rayleigh quotients which critical points correspond equation energy. An indefinite elliptic problems nonlinearities that does not satisfy Ambrosetti-Rabinowitz growth conditions also presented.

We are concerned with the following quasilinear Choquard equation: [Formula: see text] where [Formula: see text], [Formula: see text] is the p-Laplacian operator, the potential function [Formula: see text] is continuous and [Formula: see text]. Here, [Formula: see text] is the Riesz potential of order [Formula: see text]. We study the existence of weak solutions for the problem above via the mo...

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.

In this article, we study some class of fractional boundary value problem involving generalized Riemann Liouville derivative with respect to a function and the p-Laplace operator. Precisely, using variational methods combined mountain pass theorem, prove that such has nontrivial weak solution. Our main result significantly complement improves previous papers in literature.

This paper deals with a fourth-order elliptic equation Dirichlet boundary conditions. Using variant form of the mountain pass theorem, we prove existence nontrivial solutions to this problem. Furthermore, discuss fundamental properties representation solution by considering two cases. Our results not only make previous more general but also show new insights into problems.

In this paper we consider the discrete anisotropic boundary value problem using critical point theory. Thirstily we apply the direct method of the calculus of variations and the mountain pass technique in order to reach the existence of at least one non-trivial solution. Secondly we derive some version of a discrete three critical point theorem which we apply in order to get the existence of at...