# The topological degree methods for the fractional \(p(\cdot)\)-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.

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