一类抽象微分方程的周期解

Periodic Solutions of a Class of Differential Equations

考虑Ｂａｎａｃｈ空间Ｘ中的非线性微分方程ｘ＇＝Ａ（ｔ）ｘ＋ｆ（ｔ，ｘ）在关于ｆ的某些自然的条件下，利用Ｍｏｎｃｈ不动点定理证明了上述方程在给定闭凸集中的周期解的存在性。

A nonlinear differential equation in Banach space X is invsstigated,i.0x'=A(t)x+f(t,x),where A(t)andf(t ,x)are l-periodic functions in t.Under certain natural condi-tions of f,it is proved that the above-mentioned equation has at least one l-periodic solutionwhich takes its values from a given closed convex subset K of X, the chief tool used is thefixed point theorem of M6nch.The special case of A(t)≡A is also studied.