Related papers: On the Linking Principle

In this paper, we obtain a new quantitative deformation Lemma so that we can obtain more critical points, especially for supinf critical value $c_1$, $x=\varphi^{-1}(c_1)$ is a new critical point. For $infmax$ critical value $c_2$, we can…

Using the minimax technique from the critical point theory, which consists in constructing or transforming a suitable class of applications such that a critical value $c$ of a functional $f$ can be characterized as a minimax value over this…

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 in K.C. Chang, analysis…

In this paper, we apply our minimax theory ([4], [5], [6]) with the one developed by A. Moameni in [2] to formalize a general scheme giving the multiplicity of critical points. Here is a sample of application of the scheme to a critical…

The purpose of this paper is to establish a critical point theorem, which is an infinite-dimensional generalization of the classical generalized Mountain Pass Theorem of P. H. Rabinowitz \cite[Theorem 5.3]{Ra}. As application, we obtain the…

We study critical growth elliptic problems with jumping nonlinearities. Standard linking arguments based on decompositions of $H^1_0(\Omega)$ into eigenspaces of $- \Delta$ cannot be used to obtain nontrivial solutions to such problems. We…

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…

This paper is devoted to exploring a new minimax approach by introducing a characteristic mapping family which is invariant under the smooth descending flow for initial value. The minimax approach is self-contained, and its features are…

A number of landmark existence theorems of nonlinear functional analysis follow in a simple and direct way from the basic separation of convex closed sets in finite dimension via elementary versions of the Knaster-Kuratowski-Mazurkiewicz…

We study a class of $p(x)$-Kirchhoff problems which is seldom studied because the nonlinearity has nonstandard growth and contains a bi-nonlocal term. Based on variational methods, especially the Mountain pass theorem and Ekeland's…

We prove a so-called linking theorem and some of its corollaries, namely a mountain pass theorem and a three critical points theorem for Keller $ C^1$-functional on $ C^1 $- Frechet manifolds. Our approach relies on a deformation result…

In this paper, we establish some new fixed point theorems and coincidence point theorems for essential distances and $e^{0}$-metrics which generalize and improve Berinde-Berinde's fixed point theorem, Mizoguchi-Takahashi's fixed point…

With the dual variational principle and the saddle point reduction we use the abstract bifurcation theory recently developed by author in previous work to prove many new bifurcation results for solutions of four types of Hamiltonian…

This paper addresses the Mountain Pass Theorem for locally Lipschitz functions on finite-dimensional vector spaces in terms of tangencies. Namely, let $f \colon \mathbb R^n \to \mathbb R$ be a locally Lipschitz function with a mountain pass…

Using Morse theory and a new relative homological linking of pairs, we prove a ``homological linking principle'', thereby generalizing many well known results in critical point theory.

We obtain multiplicity results for a class of first-order superquadratic Hamiltonian systems and a class of indefinite superquadratic elliptic systems which lead to the study of strongly indefinite functionals. There is no assumption to the…

In this note we consider the classical variational tools like: Ekelenad's Variational Principle, Mountain Pass Lemma and some of their corollaries subject to a parameter. Next, we investigate the behaviour of critical points obtained once a…

A minimax variational principle for saddle-point solutions with prescribed energy levels is introduced. The approach is based on the development of the linking theorem to the energy level nonlinear generalized Rayleigh quotients. An…

It is established the existence and multiplicity of weak solutions for a class of nonlocal equations involving the fractional laplacian, nonlinearities with critical exponential growth and potentials this is which may change sign. The…

In this paper, we deal with the existence and multiplicity of solutions to the nonuniformly elliptic equation of the N-Lapalcian type with a potential and a nonlinear term of critical exponential growth and satisfying the…