Existence and multiplicity of solutions for some Styklov problem involving p(x)-Laplacian operator

Abstract

In this paper, we consider a class of -Laplacian problems of the form: where , is a bounded domain with Lipschitz boundary is outer unit normal derivative. The functions a, b, p, q, g and f are assumed to satisfy suitable assymptions. The existence and the multiplicity of solutions is obtained by using variational methods, and mountain pass lemma combined with Ekeland variational principle.