A degenerate elliptic system with variable exponents

TL;DR

This paper investigates a complex degenerate elliptic system with variable exponents, establishing the existence of multiple solutions using variational methods and advanced function space theory, with applications to scalar problems.

Contribution

It introduces new existence results for solutions of degenerate elliptic systems with variable exponents, employing variational techniques and weighted Sobolev spaces.

Findings

Existence of at least two distinct nontrivial weak solutions.

Existence of two nonnegative solutions for scalar problems.

Application example demonstrating the results' relevance.

Abstract

We study a degenerate elliptic system with variable exponents. Using the variational approach and some recent theory on weighted Lebesgue and Sobolev spaces with variable exponents, we prove the existence of at least two distinct nontrivial weak solutions of the system. Several consequences of the main theorem are derived; in particular, the existence of at lease two distinct nontrivial nonnegative solution are established for a scalar degenerate problem. One example is provided to showthe applicability of our results.