DCDS
Periodic and almost periodic oscillations in a delay differential equation system with time-varying coefficients
Xiao Wang Zhaohui Yang Xiongwei Liu

It is extremely difficult to establish the existence of almost periodic solutions for delay differential equations via methods that need the compactness conditions such as Schauder's fixed point theorem. To overcome this difficulty, in this paper, we employ a novel technique to construct a contraction mapping, which enables us to establish the existence of almost periodic solution for a delay differential equation system with time-varying coefficients. When the system's coefficients are periodic, coincide degree theory is used to establish the existence of periodic solutions. Global stability results are also obtained by the method of Liapunov functionals.

keywords: Almost periodic oscillation periodic oscillation global stability Liapunov functional delay differential equation

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