一类时滞偏微分方程周期解的存在性

EXISTENCE OF PERIODIC SOLUTIONS FOR DELAY PARTIAL DIFFERENTIAL EQUATION

在闭环控制系统和反馈系统中,许多量的决定不仅与当前的状态有关,而且与前期的状态有关,这反应在数学上就是时滞问题。C.C.Travis和G.F.Webb对一般时滞方程解的存在性及稳定性进行了一系列的研究(如[1],[2]),一些作者也对具体时滞方程解的存在性及性质进行了讨论(如[3])。但对时滞问题周期解的研究尚不多见。本文给出了一类较一般的时滞方程周期解的存在性。

The existence of periodic solutions for delay partial differential equations is investigated Our first objective is to give the existence theorem of solutions of abstract delay differential equations,and then prove the existence of periodic solutions in suitable spaces by Schauder fixed point theorem.Finally,we use the abstract results obtained above to prove the existence of periodic solutions for delay semilinear partial differential equations.