Pohozaev-type inequalities and nonexistence results for non $C^2$ solutions of $p(x)$-laplacian equations

Abstract

In this paper a Pohozaev type inequality is stated for variable exponent Sobolev spaces in order to prove non existence of nontrivial weak solutions for a Dirichlet problem with non-standard growth. The obtained results generalize a previous work of M. Ôtani.