Periodic solutions for \(2k\)th order ordinary differential equations with resonance (Q5945756)
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scientific article; zbMATH DE number 1657546
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Periodic solutions for \(2k\)th order ordinary differential equations with resonance |
scientific article; zbMATH DE number 1657546 |
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Periodic solutions for \(2k\)th order ordinary differential equations with resonance (English)
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29 September 2002
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higher-order differential equations
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resonance
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Hilbert space
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The author discusses the existence and uniqueness of periodic solutions to \(2k\)th-order ordinary differential equations. Based on a nonvariational version of a max-min principle, he proves, under some conditions on \(f\), that there is a unique periodic solution to the following equation NEWLINE\[NEWLINE \sum_{j=1}^k \alpha_ju^{2j}(t) + (-1)^{k+1}f(t,u(t)) = 0. NEWLINE\]NEWLINE This result extends some previous ones.
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