Multiplicity of nontrivial solutions of semilinear elliptic equations (Q1587426)
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scientific article; zbMATH DE number 1533168
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Multiplicity of nontrivial solutions of semilinear elliptic equations |
scientific article; zbMATH DE number 1533168 |
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Multiplicity of nontrivial solutions of semilinear elliptic equations (English)
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2 July 2001
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It is considered the following problem: \(-\Delta u = f(x,u)\) in \(\Omega\), \(u=0\) on \(\partial\Omega\), where \(f\) is a subcritical Carathéodory function. It is proved the existence of at least two nontrivial solutions. This paper unifies and generalizes some results from \textit{A. Castro} and \textit{A. C. Lazer} [Ann. Mat. Pura Appl., IV. Ser. 120, 113-137 (1979; Zbl 0426.35038)] as well as from \textit{N. Hirano} and \textit{T. Nishimura} [J. Math. Anal. Appl. 180, No. 2, 566-586 (1993; Zbl 0835.35052)].
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semilinear elliptic equation
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Dirichlet boundary value problem
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nontrivial solution
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reduction method
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critical point
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