On asymptotic solutions to delay differential equation with slowly varying coefficients (Q1863481)
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scientific article; zbMATH DE number 1879991
| Language | Label | Description | Also known as |
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| English | On asymptotic solutions to delay differential equation with slowly varying coefficients |
scientific article; zbMATH DE number 1879991 |
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On asymptotic solutions to delay differential equation with slowly varying coefficients (English)
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11 March 2003
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The authors study second-order weakly nonlinear ordinary delay-differential equations with slowly varying coefficients, where the nonlinear part fulfils some special assumptions. It is assumed also that the linear (unperturbed) equation obtained from the original one by dropping the nonlinear term has a set of periodic solutions of a form \(x(t)=a\cos (\omega t+\varphi)\), where \(a\) and \(\varphi\) depend on the ``slow time''. Asymptotic solutions are investigated. An algorithm for asymptotic integration of such equations is given. Its efficiency is shown by discussing several examples (including Duffing-type systems).
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