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arXiv · 1204.2163

Existence of solution to a critical equation with variable exponent

Julián Fernández Bonder·Nicolas Saintier·Analía Silva
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Abstract

In this paper we study the existence problem for the $p(x)-$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.

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Julián Fernández Bonder, Nicolas Saintier, Analía Silva. 2012-04-10. Existence of solution to a critical equation with variable exponent. https://arxiv.org/abs/1204.2163

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