Boundedness for sublinear Duffing equations with time-dependent potentials (Q1022927)
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scientific article; zbMATH DE number 5563785
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Boundedness for sublinear Duffing equations with time-dependent potentials |
scientific article; zbMATH DE number 5563785 |
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Boundedness for sublinear Duffing equations with time-dependent potentials (English)
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10 June 2009
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The author considers the sublinear second order differential equation with time-dependent potential: \[ \ddot {x} + e(t|x|^{\alpha-1}x= p(t), \tag{1} \] where \(0<\alpha<1\), \(p(t)\) and \(e(t)\) are smooth 1-periodic functions. A necessary and sufficient condition has been proved for the boundedness of all solutions of (1).
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sublinear equation
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time-dependent potentials
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boundedness of solutions
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canonical transformation
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Moser's Twist theorem
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