EXISTENCE AND MULTIPLICITY OF SOLUTIONS FOR AN ELLIPTIC EQUATION WITH -GROWTH CONDITIONS

MIHAI MIHĂILESCU

doi:10.1017/S0017089506003144

Abstract

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We study a partial differential equation on a bounded domain $\Omega\subset\mathbb{R}^N$ with a $p(x)$-growth condition in the divergence operator and we establish the existence of at least two nontrivial weak solutions in the generalized Sobolev space $W_0^{1,p(x)}(\Omega)$. Such equations have been derived as models of several physical phenomena. Our proofs rely essentially on critical point theory combined with corresponding variational techniques.

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Article contents

EXISTENCE AND MULTIPLICITY OF SOLUTIONS FOR AN ELLIPTIC EQUATION WITH $p(x)$-GROWTH CONDITIONS

Abstract

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This article has been cited by the following publications. This list is generated based on data provided by Crossref.

Article contents

EXISTENCE AND MULTIPLICITY OF SOLUTIONS FOR AN ELLIPTIC EQUATION WITH $p(x)$-GROWTH CONDITIONS

Abstract

Keywords

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