非线性二阶差分方程周期解的多重性

Multiplicity of Periodic Solutions of Second Order Nonlinear Difference Equations

变分方法是研究非线性差分方程周期解存在性的一种新的并且行之有效的方法.运用极小极大定理研究带有次线性项的二阶差分方程-Δ2un-1=μuan+f(n,un),n∈Z,α∈(0,1)证明了至少3个非平凡周期解的存在性.

The variational method is an effective method for studying the existence of periodic for nonlinear difference equations. In this paper, we use minimax theorem to study the following second order nonlinear difference equations-△^2un-1=μun^a＋f（n,un）,n∈Z,a∈（0,1） ,and obtain the existence of at least three nontrivial periodic solutions.