Periodic solutions for singular perturbations of the singular \(\phi\)-Laplacian operator (Q2853994)
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scientific article; zbMATH DE number 6215952
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Periodic solutions for singular perturbations of the singular \(\phi\)-Laplacian operator |
scientific article; zbMATH DE number 6215952 |
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17 October 2013
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singular nonlinearities
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upper solution
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lower solution
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Leray-Schauder degree
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Periodic solutions for singular perturbations of the singular \(\phi\)-Laplacian operator (English)
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The authors prove the existence of \(T\)-periodic solutions for equations of the type NEWLINE\[NEWLINE \left(\frac{u'}{\sqrt{1-(u')^2}}\right)'+r(t)u+\frac{n(t)}{u^\lambda}=e(t), NEWLINE\]NEWLINE where the functions \(r(t)\), \(n(t)\) and \(e(t)\) are continuous and \(T\)-periodic. The proofs use topological methods, lower and upper solutions, and the Leray-Schauder degree.
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