The concept of linking was developed to produce Palais-Smale (PS) sequencesG(uk)→ a, G′(uk)→ 0 for C1functionals G that separate linking sets. These sequences produce critical points if they have convergent subsequences (i.e., ifG satisfies the PS condition). In the past, we have shown that PS sequences can be obtained even when linking does not exist. We now show that such situations producemo...

In this paper, we establish a variant of Ekeland’s variational principle. This result suggest to introduce a generalization of the famous PalaisSmale condition. An example is provided showing how it is used to give the existence of minimizer for functions for which the Palais-Smale condition and the one introduced by Cerami are not satisfied.

Let X be a Finsler manifold. We prove some abstract results on the existence of critical points for strongly indefinite functionals f ∈ C1(X ,R) via a new deformation theorem. Different from the works in the literature, the new deformation theorem is constructed under a new version of Cerami-type condition instead of Palais-Smale condition. As applications, we prove the existence of multiple pe...

In this paper we give two existence theorems for a class of elliptic problems in an Orlicz-Sobolev space setting concerning both the sublinear and the superlinear case with Neumann boundary conditions. We use the classical critical point theory with the Cerami (PS)-condition.

Existence and multiplicity results are obtained for superlinear p-Laplacian equations without the Ambrosetti and Rabinowitz condition. To overcome the difficulty that the Palais-Smale sequences of the EulerLagrange functional may be unbounded, we consider the Cerami sequences. Our results extend the recent results of Miyagaki and Souto [ J. Differential Equations 245 (2008), 3628–3638].

In this paper we consider two elliptic problems. The first one is a Dirichlet problem while the second is Neumann. We extend all the known results concerning Landesman-Laser conditions by using the Mountain-Pass theorem with the Cerami (PS) condition.

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.

A general method is given in order to guarantee at least one nontrivial solution, as well as infinitely many radially symmetric solutions, for an abstract class of hemivariational inequalities. This abstract class contains some special cases studied by many authors. We remark that, differently from the classical literature, in the proofs we use the Cerami compactness condition and the principle...