Existence and uniqueness of solutions of a nonlocal problem involving the p(x)-Laplacian

Abstract

The object of this paper is to study a nonlocal problem involving the p(x)-Laplacian where nonlinearities $f$ do not necessarily satisfy the classical conditions, such as Ambrosetti-Rabinowitz condition, but are limited by functions that do satisfy some specific conditions. By using the direct variational approach and the theory of the variable exponent Sobolev spaces, the existence and uniqueness of solutions is obtained.