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Multiplicity Results for Periodic Solutions to Second-Order Difference Equations

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Abstract

By using the Z p geometrical index theory, some sufficient conditions on the multiplicity results of periodic solutions to the second-order difference equations

$$\Delta^2x_{n-1}+f(x_n)=0$$

are obtained. By two examples, we show that our results are the best possible in the sense that the lower bound of the number of periodic solutions cannot be improved.

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Authors and Affiliations

  1. College of Mathematics and Information Sciences, Guangzhou University, Guangzhou, 510006, P. R. China

    Zhiming Guo & Jianshe Yu

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  1. Zhiming Guo
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  2. Jianshe Yu
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Correspondence to Jianshe Yu.

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Guo, Z., Yu, J. Multiplicity Results for Periodic Solutions to Second-Order Difference Equations. J Dyn Diff Equat 18, 943–960 (2006). https://doi.org/10.1007/s10884-006-9042-1

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  • DOI: https://doi.org/10.1007/s10884-006-9042-1

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