The concentration-compactness principle for variable exponent spaces and applications

TL;DR

This paper extends the concentration-compactness principle to variable exponent spaces and applies it to establish existence results for the p(x)-Laplacian with critical growth.

Contribution

It generalizes the classical concentration-compactness principle to variable exponent spaces and demonstrates its application to nonlinear PDEs with critical growth.

Findings

Extended concentration-compactness principle to variable exponent spaces

Proved existence results for p(x)-Laplacian with critical growth

Provided new tools for nonlinear analysis in variable exponent settings

Abstract

In this paper we extend the well-known concentration -- compactness principle of P.L. Lions to the variable exponent case. We also give some applications to the existence problem for the $p(x)-$Laplacian with critical growth.