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

作　　者：吴汉忠[1] 

机构地区：[1]安徽大学数学系

出　　处：《安徽大学学报（自然科学版）》1991年第1期10-15,共6页Journal of Anhui University(Natural Science Edition)

基　　金：国家自然科学資金资助

摘　　要：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.

关 键 词：无穷时滞 相空间 存在性 可微性 

分 类 号：O175.1[理学—数学]