On the existence of periodic solutions for \(p\)-Laplacian generalized Liénard equation (Q703409)
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scientific article; zbMATH DE number 2126025
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On the existence of periodic solutions for \(p\)-Laplacian generalized Liénard equation |
scientific article; zbMATH DE number 2126025 |
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On the existence of periodic solutions for \(p\)-Laplacian generalized Liénard equation (English)
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11 January 2005
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The authors consider a generalized Liénard ODE of second order with variable terms and a variable `shifted' argument. They establish an abstract non-constructive existence theorem for periodic solutions within the framework of Banach space theory. The key of the proof is based on the extension of the linear operator equation \(Lx=0\) to the nonlinearly perturbed case \(Lx=Nx\) (`Continuation principle'). No concrete equation is solved, and no uniqueness theorem is formulated.
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Banach spaces
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generalized Liénard ordinary differential equation
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existence theorem
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