Limits of solutions to a nonlinear second-order ODE (Q435090)
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scientific article; zbMATH DE number 6057296
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Limits of solutions to a nonlinear second-order ODE |
scientific article; zbMATH DE number 6057296 |
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Limits of solutions to a nonlinear second-order ODE (English)
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16 July 2012
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second-order ODE
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Lyapunov function
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homoclinic solution
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The paper deals with the differential equation NEWLINE\[NEWLINE\ddot{x}+2f(t)\dot{x}+\beta(t)x+g(t,x)=0.NEWLINE\]NEWLINE Based on the method of Lyapunov functions and employing some differential inequalities, the existence of homoclinic orbits is proven.
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