Existence of solution to a critical equation with variable exponent

Details Existence of solution to a critical equation with variable exponent Existence of solution to a critical equation with variable exponent

2012-04-10

arxiv.org/abs/1204.2163v1

Mathematics

Analysis of PDEs

Scientific paper

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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