Multiple solutions for quasilinear elliptic systems involving variable exponents

TL;DR

This paper proves the existence of multiple solutions for a class of quasilinear elliptic systems involving variable exponent Laplacian operators, using sub-supersolution and topological degree methods.

Contribution

It introduces a novel approach combining sub-supersolution and Leray--Schauder degree to establish multiple solutions for variable exponent elliptic systems.

Findings

Multiple solutions are proven to exist for the system.

The methods can handle nonvariational structures.

The approach extends previous results to variable exponent contexts.

Abstract

We establish the existence of multiple solutions for a nonvariational elliptic systems involving $p(x)$-Laplacian operator. The approach combines the methods of sub-supersolution and Leray--Schauder topological degree.