Existence of solution to a critical equation with variable exponent
Analysis of PDEs
2013-11-28 v1
Abstract
In this paper we study the existence problem for the Laplacian operator with a nonlinear critical source. We find a local condition on the exponents ensuring the existence of a nontrivial solution that shows that the Pohozaev obstruction does not holds in general in the variable exponent setting. The proof relies on the Concentration--Compactness Principle for variable exponents and the Mountain Pass Theorem.
Keywords
Cite
@article{arxiv.1204.2163,
title = {Existence of solution to a critical equation with variable exponent},
author = {Julián Fernández Bonder and Nicolas Saintier and Analía Silva},
journal= {arXiv preprint arXiv:1204.2163},
year = {2013}
}