This study concerns the existence and multiplicity of positive weak solutions for a class of semilinear elliptic systems with nonlinear boundary conditions. Our results is depending on the local minimization method on the Nehari manifold and some variational techniques. Also, by using Mountain Pass Lemma, we establish the existence of at least one solution with positive energy.

this study concerns the existence and multiplicity of positive weak solutions for a class ofsemilinear elliptic systems with nonlinear boundary conditions. our results is depending onthe local minimization method on the nehari manifold and some variational techniques. alsoby using mountain pass lemma, we establish the existence of at least one solution withpositive energy.

Abstract This work treats a typical type of quasilinear system concerning critical Sobolev growth. In the light Lions principle and Mountain pass lemma, mountain pass-type solutions can be derived.

We present a version of the classical Mountain Pass Lemma and explain how to combine it with constraint qualifications to prove that nonlinear programming problems have a unique local minimizer.

Abstract In this article, we study a class of new p ( x )-Kirchhoff problem without satisfying the Ambrosetti-Rabinowitz type growth condition. Under some suitable superliner conditions, introduce methods to show boundedness Cerami sequences. By using mountain pass lemma and symmetric lemma, prove that has nontrivial weak solution infinitely many solutions.

The classical Mountain Pass Lemma of Ambrosetti-Rabinowitz has been studied, extended and modified in several directions. Notable examples would certainly include the generalization to locally Lipschitz functionals by K. C. Chang, analyzing structure critical set mountain pass theorem works Hofer, Pucci-Serrin Tian, extension Ghoussoub-Preiss closed subsets a Banach space with recent variations...

Variational methods find solutions of equations by considering a solution as a critical point of an appropriately chosen function. Local minima and maxima are well-known types of critical points. We explore methods for finding critical points that are neither local maxima or minima, but instead are mountain passes or saddle points. Criteria for the existence of minima or maxima are well-known, ...