二阶渐近线性差分方程组周期解的多重性

Multiplicity of Periodic Solutions for Second-Order Asymptotically Linear Difference System

利用临界点理论和Morse理论,研究一类二阶渐近线性差分方程组非平凡周期解的存在性和多重性,通过计算相应泛函在零点及无穷远点的临界群,结合Morse不等式,证明了当非线性项满足一定条件时,该差分方程组至少存在一个或两个非平凡周期解。

In this paper,we study the existence and multiplicity of nontrivial periodic solutions for second-order asymptotically linear difference system by using the critical point theory and the Morse theory.Based on computation of the critical groups of the corresponding functional at zero and infinity and the Morse inequality,it is proved that the difference system has at least one or two nontrivial periodic solutions when the nonlinear terms satisfy certain conditions.