On the superlinear Steklov problem involving the $p(x)$-Laplacian

Abstract

This paper is concerned with the existence and multiplicity of solutions for $p(x)$-Laplacian Steklov problem without the well-known Ambrosetti-Rabinowitz type growth conditions. By means of critical point theorems with Cerami condition, under weaker conditions, existence and multiplicity results of the solutions are proved.

Keywords

• variational method
• nonstandard growth conditions
• generalized sobolev spaces
• cerami condition