Multiple solutions of nonlinear elliptic Dirichlet problems in exterior domains (Q1961255)
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scientific article; zbMATH DE number 1389520
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Multiple solutions of nonlinear elliptic Dirichlet problems in exterior domains |
scientific article; zbMATH DE number 1389520 |
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Multiple solutions of nonlinear elliptic Dirichlet problems in exterior domains (English)
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26 June 2000
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The authors consider the Dirichlet problem for the equation \(-\Delta u + \lambda^2u=u^{p-1}\) in an exterior domain \(\Omega\), with a subcritical \(p\). It is shown that there exist at least \(2k-1\) distinct positive solutions, provided the complement of \(\Omega\) consists of \(k\) sufficiently large connected components.
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nonlinear elliptic Dirichlet problems
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exterior domains
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multiple positive solutions
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