Multiplicity results for periodic solutions to a class of second order delay differential equations (Q618973)
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scientific article; zbMATH DE number 5837958
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Multiplicity results for periodic solutions to a class of second order delay differential equations |
scientific article; zbMATH DE number 5837958 |
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Multiplicity results for periodic solutions to a class of second order delay differential equations (English)
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17 January 2011
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Though there are lots of results on the existence of periodic solutions to delay differential equations, results on the multiplicity of peridoic solutions are scarce. In this paper, the authors study the following second order delay differential equation \[ x''(t)=-f(x(t), x(t-\tau)). \] By using critical point theory and \(S^1\) geometric index theory, they establish some new results on the existence and multiplicity of periodic solutions.
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second order delay differential equation
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multiple periodic solutions
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Hamiltonian system
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critical point theory
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\(S^1\) geometrical index theory
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