Periodic and subharmonic solutions for Duffing equation with a singularity (Q414767)
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scientific article; zbMATH DE number 6033396
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Periodic and subharmonic solutions for Duffing equation with a singularity |
scientific article; zbMATH DE number 6033396 |
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Periodic and subharmonic solutions for Duffing equation with a singularity (English)
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11 May 2012
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Duffing equation
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harmonic and subharmonic solution
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superlinear
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singularity
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Poincaré-Birkhoff twist theorem
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The authors study the existence and multiplicity of periodic and subharmonic solutions of the second-order differential equation NEWLINE\[NEWLINEx''+g(x)=p(t),NEWLINE\]NEWLINE where \(p\) is a \(T\)-periodic force and \(g\) presents a strong singularity of repulsive type at the origin. The method of proof combines a generalized version of the Poincaré-Birkhoff twist theorem with a qualitative analysis of the phase-plane properties.
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