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Zbl 1160.39311
Yu, Jianshe; Shi, Haiping; Guo, Zhiming
Homoclinic orbits for nonlinear difference equations containing both advance and retardation. (English)
[J] J. Math. Anal. Appl. 352, No. 2, 799-806 (2009). ISSN 0022-247X

Summary: We discuss how to use the critical point theory to study the existence of a nontrivial homoclinic orbit for nonlinear difference equations containing both advance and retardation without any periodic assumptions. Moreover, if the nonlinearity is an odd function, the existence of an unbounded sequence of homoclinic orbits is obtained.
MSC 2000:
*39A11 Stability of difference equations

Keywords: homoclinic orbits; nonlinear difference equations; advance and retardation; variational structure; critical point

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