无穷时滞RFDE解的存在性及其对初始函数的可微性

The Existences and Differentiabilities of Solutions of Functional-differential Equations with Infinite Delay

本文建立了无穷时滞RFDE解的存在性定理,改进了文[2]之定理1,并建立了无穷时滞RFDE解对初始函数的可微性定理,完善了无穷时滞RFDE解的基本理论。同时,有界时滞RFDE作为无穷时滞RFDE之特殊情形,本文的结果改进了文[3]关于有界时滞RFDE解的存在性定理(p37),并对文[3]关于有界时滞RFDE解对初始函数可微性定理(pp46-47)给出一严密证明,纠正了文[3]中一个易忽视的证明错误。

An existence theorem of solutions of functional- differential equations with infinite delay,which improves theorem 1 In the paper[2],and a differentiability theorem of solutions of FDEs with infinite delay,which perfects the basic theory of solutions of FDEs with infinite delay are proved. Moreover, theorem 1 in this paper improres theorem 2.1 in the book[3] about the existences of solutions of FDEs with bounded delay,and theorem 2 in this paper gives a strict Proof of theorem 4.1 in the book[3] about the differentiabilities of solutions of FDEs with bounded delay.