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Multiplicity Results for Periodic Solutions to Second-Order Difference Equations

Authors:

Zhiming Guo Jianshe Yu

Institution:

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

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.

Keywords:

Second-order difference equations periodic solution critical point Z p index theory

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