The topological degree methods for the fractional p(⋅)-Laplacian problems with discontinuous nonlinearities

Abstract

In this article, we use the topological degree based on the abstract Hammerstein equation to investigate the existence of weak solutions for a class of elliptic Dirichlet boundary value problems involving the fractional p(x)-Laplacian operator with discontinuous nonlinearities. The appropriate functional framework for this problems is the fractional Sobolev space with variable exponent.

Keywords

• fractional p(x)-laplacian
• weak solution
• discontinuous nonlinearity
• topological degree theory