Nonlinear problem involving the fractional p(x)-Laplacian operator by Topological degree

TL;DR

This paper investigates nonlinear problems with the fractional p(x)-Laplacian operator, establishing the existence of solutions using topological degree theory within fractional Sobolev spaces with variable exponents.

Contribution

It introduces a novel application of Berkovits degree theory to fractional p(x)-Laplacian problems in variable exponent Sobolev spaces.

Findings

Existence of nontrivial weak solutions proven

Application of topological degree theory to fractional operators

Framework established in fractional Sobolev spaces with variable exponents

Abstract

This paper is concerned with the study of a nonlinear problems involving the fractional p(x)-Laplacian operator. By means of the Berkovits degree theory, we prove the existence of nontrivial weak solutions for this problem. The appropriate functional framework for this problems is the fractional Sobolev spaces with variable exponent.