具有超前和滞后的2n阶泛函差分方程的周期解

Periodic Solutions of a 2nth-Order Functional Difference Equation Containing Both Advance and Retardation

研究具有超前和滞后的2n阶泛函差分方程周期解的存在性.将差分方程周期解的存在性问题转化成相应的泛函临界点的存在性问题.利用临界点理论,获得了此方程至少存在2个非平凡周期解的充分条件,推广并改进了已有文献的一些结论.

The existence of periodic solutions to a 2nth-order functional difference equation containing both advance and retardation is studied. By using the critical point theory and transferring the existence of the periodic solutions of the equations into the existence of critical points of some functional, a sufficient condition for the existence of at least two nontrivial periodic solutions is obtained. Our result extends and improves some conclusions in the existing literatures.