一类扰动系统的多重周期解

Multiple periodic solutions of a class of differential equations with perturbations

论文研究一类带依赖于时间变量和小参数的扰动项的时滞微分方程具有给定周期的多重周期解的存在性,将此类微分系统转化成Hamilton系统,运用渐进凸Hamilton系统理论及Morse指标理论的一些结果得到了此类扰动系统的多重周期解的存在性,此结论推广了此类方程在没有扰动项时的结果.

In this paper, the existence of multiple periodic solutions of a class of differential delay equations with perturbations depending on time variable and little parameter was studied. The differential systems were changed to Hamihonian systems. By using some results in the theory of convex asymptotically linear Hamihonian systems and Morse theory, the existence of multiple periodic solutions of the systems was gotten. The conclusion extended some results about the systems without the perturbations.