On bounded and time-periodic solutions of nonlinear wave equations (Q5945763)
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scientific article; zbMATH DE number 1657553
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On bounded and time-periodic solutions of nonlinear wave equations |
scientific article; zbMATH DE number 1657553 |
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On bounded and time-periodic solutions of nonlinear wave equations (English)
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13 November 2002
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at least one time-periodic solution
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uniqueness
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A nonlinear wave equation of the form: NEWLINE\[NEWLINE u_{tt} - u_{ss} = g(t,s,u) + g_1(u) u_t NEWLINE\]NEWLINE on an infinite strip \(\mathbb{R} \times [0,a]\) is studied. Suffient conditions are given in terms of the structural properties of the functions \(g\) and \(g_1\) for the problem to possess at least one time-periodic solution provided \(g\) is periodic in \(t\). Uniqueness of these solutions is also studied.
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