Periodic solutions of a second order nonlinear system (Q1378669)
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scientific article; zbMATH DE number 1115510
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Periodic solutions of a second order nonlinear system |
scientific article; zbMATH DE number 1115510 |
Statements
Periodic solutions of a second order nonlinear system (English)
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11 October 1998
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The existence of periodic solutions of the Liénard system \[ x''(t)+ d[\text{grad }F(x(t))]/dt+ g(t,x(t))= e(t), \] where \(x\) is an \(n\)-dimensional vector and \(e(t)\) and \(g(t, x(t))\) are \(2\pi\)-periodic in \(t\), is investigated for various asymptotic behaviours of \(g\). Conditions for periodic solutions with detailed conditions are given in four theorems.
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existence
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Liénard system
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periodic solutions
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