一类奇异摄动系统的周期解
Periodic solutions for a class of singulary perturbated systems
摘要：
本文给出了一类一阶奇摄动微分系统在$e>0$充分小的情况下，在给定区域$U$中存在给定周期$T>0$的周期解的条件.这里$e>0$是扰动参数。我们的方法，基于拓扑度理论和平均理论，允许削弱[K.R. Schneider，Vibrational control of奇异摄动系统，in“Lectures Notes in Control and Information Science”，259，397-408，Springer，London，2001，Theorem 2]，在此基础上证明了周期解的存在性。
英文摘要：
In this paper we provide conditions to ensure the existence, for $e>0$ sufficiently small, of periodic solutions of given period $T>0$ in a prescribed domain $U$ for a class of singularly perturbed first order differential systems. Here $e>0$ is the perturbation parameter. Our approach, based on the topological degree theory and the averaging theory, permits to weaken the conditions in [K.R. Schneider, Vibrational control of singularly perturbed systems, in "Lectures Notes in Control and Information Science", 259, 397-408, Springer, London, 2001, Theorem 2] under which the existence of periodic solutions is proved.
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