On the existence of periodic solutions for the quasi-linear third-order differential equation (Q5946938)
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scientific article; zbMATH DE number 1660599
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On the existence of periodic solutions for the quasi-linear third-order differential equation |
scientific article; zbMATH DE number 1660599 |
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On the existence of periodic solutions for the quasi-linear third-order differential equation (English)
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15 October 2002
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nonlinear equations
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periodic solutions
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topological degree
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homotopy invariance
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The following third-order quasi-linear differential equation NEWLINE\[NEWLINE x'''+k^2 x'= \epsilon f(x,x',x'') NEWLINE\]NEWLINE is considered. Simple conditions for the existence of a periodic solution are obtained on the base of the implicit function theorem. An example is given, and the validity of the condition for the parameter-free problem, that is for \(\epsilon=1\), is discussed.
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