Existence of weak solutions of the fractional p(x,y)$$ p\left(x,y\right) $$‐Laplacian problem by topological degree

Abstract

In this paper, we prove the existence result of weak solutions to a class fractional ‐Laplacian problems involving the nonlocal integro‐differential operator of elliptique type . The main tool used here is based on the topological degree theory combined with the theory fractional Sobolev spaces with variable exponent. Our results generalize and improve the existing results.