In this note we use variational arguments {namely Ekeland's Principle and the Mountain Pass Theorem{ to study the equation ?u + a(x)u = u q + u 2 ?1 in R N : The main concern is overcoming compactness diiculties due both to the unboundedness of the domain R N , and the presence of the critical exponent 2 = 2N=(N ? 2).

The main purpose of this paper is to establish a three critical points result without assuming the coercivity of the involved functional. To this end, a mountain-pass theorem, where the usual Palais-Smale condition is not requested, is presented. These results are then applied to prove the existence of three solutions for a two-point boundary value problem with no asymptotic conditions.

We study an eigenvalue problem involving variable exponent growth conditions and a non-local term, on a bounded domain Ω ⊂ RN . Using adequate variational techniques, mainly based on the mountain-pass theorem of A. Ambrosetti and P. H. Rabinowitz, we prove the existence of a continuous family of eigenvalues lying in a neighborhood at the right of the origin. Mathematics subject classification (...

During the last twenty years, many minimax theorems that have proved to be very useful tools in finding critical points of functionals have been established. They have all in common a geometric intersection property known as the linking principle. Our purpose in this paper is to give a linking theorem that strengthens and unifies some of these works. We think essentially to Ambrosetti-Rabinowit...

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...

We develop a min–max theory for asymptotically conical self-expanders of mean curvature flow. In particular, we show that given two distinct strictly stable are asymptotic to the same cone and bound domain, there exists new self-expander trapped between two.

We study the existence of homoclinic solutions for semilinear p−Laplacian difference equations with periodic coefficients. The proof of the main result is based on Brezis–Nirenberg’s Mountain Pass Theorem. Several examples and remarks are given.

In this paper hemivariational inequality with nonhomogeneous Neumann boundary condition is investigated. The existence of infinitely many small solutions involving a class of p(x)−Laplacian equation in a smooth bounded domain is established. Our main tool is based on a version of the symmetric mountain pass lemma due to Kajikiya and the principle of symmetric criticality for a locally Lipschitz...