p(x, ·)-Kirchhoff Type Problem Involving the Fractional p(x)-Laplacian Operator with Discontinuous Nonlinearities

Abstract

The purpose of this paper is mainly to investigate the existence of weak solution of the stationary Kirchhoff type equations driven by the fractional  $p(x)$-Laplacian operator with discontinuous nonlinearities   for a class of elliptic Dirichlet boundary value problems. By using the topological degree based on the abstract Hammerstein equation, we conduct our existence analysis. The fractional Sobolev space with variable exponent provides an effective functional framework for these situations.