Multiplicity of forced oscillations for scalar differential equations (Q2717773)
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scientific article; zbMATH DE number 1605717
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Multiplicity of forced oscillations for scalar differential equations |
scientific article; zbMATH DE number 1605717 |
Statements
18 June 2001
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forced oscillations
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multiplicity of periodic solutions
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Multiplicity of forced oscillations for scalar differential equations (English)
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Here, the authors study the multiplicity of periodic solutions to the following equation NEWLINE\[NEWLINE\ddot x = g(x) + \varepsilon f(t, x, \dot x). NEWLINE\]NEWLINE Under the following assumptions: (1) \(g(x)\) changes sign at \(n\) zeros; (2) the corresponding autonomous equation is not isochronous; (3) the functions \(g(x)\) and \(f(t,x,\dot x)\) are \(C^1\) and continuous, respectively, they prove that there are at least \(n\) forced oscillations for \(\varepsilon\) sufficiently small.
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