On the existence of nontrivial solutions of inequalities in Orlicz-Sobolev spaces (Q449523)
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scientific article; zbMATH DE number 6074673
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On the existence of nontrivial solutions of inequalities in Orlicz-Sobolev spaces |
scientific article; zbMATH DE number 6074673 |
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On the existence of nontrivial solutions of inequalities in Orlicz-Sobolev spaces (English)
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30 August 2012
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nonsmooth functional
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mountain pass theorem
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Palais-Smale condition
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Orlicz-Sobolev space
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The paper deals with semilinear elliptic equations NEWLINE\[NEWLINE \text{div} (a(|\nabla u|)\nabla u) +\partial_u G(x,u) \ni 0.NEWLINE\]NEWLINE Conditions are given on \(a\) and \(G\) so that the problem admits nontrivial solutions with zero boundary conditions in domains \(\Omega \in \mathbb{R}^N\) after it has been reformulated as a variational inequality. Also, when \(G\) is an even function in \(u\), conditions are given so that the problem admits infinitely many solutions.
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