Existence and multiplicity of periodic solutions of the second-order differential equations with jumping nonlinearities (Q1862922)
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scientific article; zbMATH DE number 1885860
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Existence and multiplicity of periodic solutions of the second-order differential equations with jumping nonlinearities |
scientific article; zbMATH DE number 1885860 |
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Existence and multiplicity of periodic solutions of the second-order differential equations with jumping nonlinearities (English)
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13 January 2004
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The author studies the existence and multiplicity of periodic solutions to the following equation \[ \ddot u + au^+ - bu^- +g(u) = p(t). \] Under some conditions on \(g\), he proves that there is at least one harmonic solution and determines the multiplicity of subharmonics. The proof is based on the Poincaré- Birkhoff twist theorem and on estimates on the time map.
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periodic solutions
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jumping nonlinearities
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time map
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