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

TL;DR

This paper establishes a Pohozaev-type inequality for variable exponent Sobolev spaces to prove the nonexistence of nontrivial solutions for certain p(x)-Laplacian equations with non-standard growth.

Contribution

It generalizes previous results by deriving a Pohozaev inequality applicable to variable exponent spaces, leading to new nonexistence results.

Findings

Proves nonexistence of solutions under specific conditions

Extends Pohozaev inequalities to variable exponent Sobolev spaces

Generalizes prior work by M. Otani

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. \^{O}tani.