Periodic solutions to nonlinear wave equations with \(x\)-dependent coefficients at resonance (Q1799896)
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scientific article; zbMATH DE number 6958780
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Periodic solutions to nonlinear wave equations with \(x\)-dependent coefficients at resonance |
scientific article; zbMATH DE number 6958780 |
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Periodic solutions to nonlinear wave equations with \(x\)-dependent coefficients at resonance (English)
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19 October 2018
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This paper concerns the existence problem for a time-periodic problem for a system of semilinear wave equations on an interval, which is at resonance, in the sense that the derivative of the nonlinearity is allowed to interact with two consecutive eigenvalues of the linear part. Under certain restriction on the interaction, existence and uniqueness of a solution is proved. The proof uses the Galerkin method and a global inversion theorem.
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unique existence
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Galerkin method
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global inversion theorem
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0.9516898
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0.95089376
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0.9469409
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0.93972194
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0.93808913
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