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Existence of Solution to a Critical Equation with Variable Exponent by Bonder, Julián Fernández; Saintier, Nicolas; Silva, Analía is a scholarly article available to read on EtoBox.

What is Existence of Solution to a Critical Equation with Variable Exponent about?

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.

Author

Bonder, Julián Fernández; Saintier, Nicolas; Silva, Analía

Published

2012

Language

EN