The periodic problem for curvature-like equations with asymmetric perturbations (Q639506)
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scientific article; zbMATH DE number 5949065
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | The periodic problem for curvature-like equations with asymmetric perturbations |
scientific article; zbMATH DE number 5949065 |
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The periodic problem for curvature-like equations with asymmetric perturbations (English)
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22 September 2011
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Non-existence, existence and multiplicity of \(T\)-periodic solutions for the prescribed curvature-like equation \[ -{\left({u'}{\sqrt{a^2+{u'}^2}}\right)}' =f(t,u) \] is studied. The case \(a=0\) is allowed; thus, the results are valid for the \(1\)-Laplace equation. The Sobolev space \(W_T^{1,1}(0,T)\) is replaced by the space \(BV(0,T)\) (of functions of bounded variation).
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quasilinear ordinary differential equation
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prescribed curvature equation
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1-Laplace equation
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periodic problem
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Ahmad-Lazer-Paul condition
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Hammerstein condition
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Landesman-Lazer condition
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