抽象泛函微分方程解的存在性

The Existence of Solutions of Abstract Functional Differential Equations

设X是一Banach空间,r≥0,f:Ω(?)R×C([-r,0],X)→X考虑泛函微分方程x’(t)=f(t,x_t).主要结果指明:若f满足一定集压缩性条件,则初值问题“x’(t)=f(t,x_t),x_ο=(?)”有解.所用的主要工具是Kuratowski非紧测度.

Let X be a Banach space,r≥0,and f:Ω R×C([-r,0],X)→X.The functional differential equation x'(t)=f(t,xt) is considered. The main result obtained shows that if certain set-contractivity conditions are satisfied by f,then the initial value problem "x' (t)=f(t,xt), xσ= " has a solution. The main tool used is the Kuratowski measure of non-compactness.