, Volume 18, Issue 4, pp 943-960
Date: 02 Sep 2006

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.