Homoclinic orbits for a class of nonlinear difference equations (Q2811499)
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scientific article; zbMATH DE number 6592144
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Homoclinic orbits for a class of nonlinear difference equations |
scientific article; zbMATH DE number 6592144 |
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10 June 2016
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nonlinear difference equations
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homoclinic orbits
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discrete variational theory
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Homoclinic orbits for a class of nonlinear difference equations (English)
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Consider the forward and backward difference equation of the form: NEWLINE\[NEWLINE\Delta(p_{n}(\Delta u_{n-1})^{\delta})-q_{n}u_{n}^{\delta}+f(n,u_{n+1},u_{n},u_{n-1})=0,\quad n\in\mathbb Z\tag{1}NEWLINE\]NEWLINE Under a number of hypotheses it is shown that (1) has a nontrivial homoclinic orbit. An example is also given. (See also a related paper by the same authors [Hokkaido Math. J. 45, No. 1, 109--126 (2016; Zbl 1345.39008)]).
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