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Zbl 1107.39022
Ma, Manjun; Guo, Zhiming
Homoclinic orbits for second order self-adjoint difference equations. (English)
[J] J. Math. Anal. Appl. 323, No. 1, 513-521 (2006). ISSN 0022-247X

The authors use variational methods to study the existence of nontrivial homoclinic orbits for a nonlinear difference equation. Such solutions were first discovered by Poincaré in 1899. They are also called doubly asymptotic solutions. The proof of the main result in this paper is based on the mountain pass theorem.
[H. B. Bouzahir (Agadir)]

MSC 2000:: *39A12 Discrete version of topics in analysis
39A11 Stability of difference equations
37C29 Homoclinic and heteroclinic orbits

Keywords: doubly asymptotic solutions; homoclinic orbits; discrete variational methods; nonlinear difference equation; mountain pass theorem

Cited in: Zbl 1171.39005

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