积分-微分方程周期解的存在性(英文)

Periodic Solutions of Nonlinear Integro-differential Equations

以(Cg,|.|g)为相空间研究了具有无限时滞积分-微分方程周期解的存在性,利用Schauder-Tychonov不动点定理证明了方程解的g一致有界解有界性和g一致最终有界性蕴含周期解的存在性,推广了已有的一些结论.

The existence of periodic solutions of nonlinear integro-differential equations with infinite delay is studied in the phase space （ Cg, I·Ig ）. It has been proved that g - uniformly bounded and g - uniformly ultimately bounded solutions imply the exist-ence of periodic solutions using fixed point theorem of Schauder-Tychonov. Some known results are generalized.