Existence results for degenerate $p(x)$-Laplace equations with Leray-Lions type operators

TL;DR

This paper establishes existence results for degenerate variable exponent p-Laplace equations with Leray-Lions operators, analyzing growth conditions and employing variational methods.

Contribution

It provides new existence theorems for degenerate p(x)-Laplace equations under various growth and degeneracy conditions, using direct and critical point methods.

Findings

Existence results under specific degeneracy conditions

Analysis of growth rate relationships between operators and nonlinearities

Application of variational and critical point theories

Abstract

We show the various existence results for degenerate $p(x)$-Laplace equations with Leray-Lions type operators. A suitable condition on degeneracy is discussed and proofs are mainly based on direct methods and critical point theories in Calculus of Variations. In particular, we investigate the various situations of the growth rates between principal operators and nonlinearities.