A sub-supersolution method for a class of nonlocal system involving the p(x)-Laplacian operator and applications

TL;DR

This paper introduces a new sub-supersolution method to establish the existence of solutions for nonlocal systems involving the variable exponent p(x)-Laplacian operator, expanding analytical tools for such complex PDEs.

Contribution

It develops a novel sub-supersolution approach specifically tailored for nonlocal p(x)-Laplacian systems, providing a new framework for proving solution existence.

Findings

Established existence results for a class of nonlocal p(x)-Laplacian systems.

Developed a new sub-supersolution theorem applicable to variable exponent operators.

Demonstrated applications of the method to specific nonlocal problems.

Abstract

In the present paper we study the existence of solutions for a class of nonlocal system involving the p(x)-Laplacian operator. The approach is based on a new sub-supersolution result.