Résumé: In this paper we consider a boundary value problem for the p(x)-Laplacian under nonlinear Neumann type boundary condition. We establish the existence of a global minimum for the Euler-Lagrange energy. A second weak solution is obtained by the Mountain-Pass Theorem.

Résumé: We consider a resonance problem driven by a nonhomogeneous operator and a Carathéodory reaction f(.,.). Using a variant of the monotone operator theorem, we show that the problem has at least a nontrivial solution.

Résumé: We study the Dirichlet boundary value problem for the p(x)- Laplacian We introduce a new variational technic that allows us to investigate problem without need of the Ambrosetti and Rabinowitz condition on the nonlinearity f.

Résumé: This paper concerns the study of a nonlinear eigenvalue problem for the (p, q)−Laplacian with a positive weight −
pu −
qu = λg(x)|u|^(p−2)u in RN. Using the Mountain-Pass Theorem, we show the existence of a continuous set of positive eigenvalues.

Résumé: This paper, following the theory of partial differential equations on variable exponent Sobolev spaces, is mainly concerned with the p(x)-Laplacian eigenvalue problem with a weight function on image. The results show that the spectrum of such problems contains a continuous family of eigenvalues.

Résumé: A positive solution of a semilinear elliptic partial differential equation over the whole of Rn image is shown to be a regular decay function, by means of the Sobolev embedding theorem and a bootstrap argument.

Résumé: The goal of this paper is to study semilinear elliptic indefinite weight problems defined in Rn where the weight function g changes sign in Rn. Under some suitable conditions on q(x), g(x), f(x, u) the authors prove the existence of exactly one positive solution.

Résumé: The purpose of the present paper is to investigate the existence of principal eigenvalues for linear elliptic problems in R2