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Homoclinic Orbits of Nonlinear Functional Difference Equations

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Abstract

In this paper, by using the critical point theory, we obtain the existence of a nontrivial homoclinic orbit which decays exponentially at infinity 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 nontrivial homoclinic orbits which decay exponentially at infinity is obtained.

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  1. College of Mathematics and Econometrics, Hunan University, Changsha, 410082, People’s Republic of China

    Haiping Shi

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  1. Haiping Shi
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Shi, H. Homoclinic Orbits of Nonlinear Functional Difference Equations. Acta Appl Math 106, 135–147 (2009). https://doi.org/10.1007/s10440-008-9331-2

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  • DOI: https://doi.org/10.1007/s10440-008-9331-2

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