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Homoclinic solutions in periodic difference equations with saturable nonlinearity

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Abstract

In this paper, a periodic difference equation with saturable nonlinearity is considered. Using the linking theorem in combination with periodic approximations, we establish sufficient conditions on the nonexistence and on the existence of homoclinic solutions. Our results not only solve an open problem proposed by Pankov, but also greatly improve some existing ones even for some special cases.

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Authors and Affiliations

  1. School of Mathematics and Information Science, Guangzhou University, Guangzhou, 510006, China

    Zhan Zhou & JianShe Yu

  2. Department of Mathematics, Wilfrid Laurier University, Waterloo, N2L 3C5, Canada

    YuMing Chen

Authors
  1. Zhan Zhou
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  2. JianShe Yu
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  3. YuMing Chen
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Correspondence to Zhan Zhou.

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Zhou, Z., Yu, J. & Chen, Y. Homoclinic solutions in periodic difference equations with saturable nonlinearity. Sci. China Math. 54, 83–93 (2011). https://doi.org/10.1007/s11425-010-4101-9

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  • DOI: https://doi.org/10.1007/s11425-010-4101-9

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