EXPONENTIAL STABILITY FOR AUTONOMOUS LINEAR FUNCTIONAL DIFFERENTIAL EQUATIONS WITH INFINITE RETARDATIONS  

作　　者：黄发伦 

机构地区：[1]Department of Mathematics, Sichuan University, Chengdu

出　　处：《Science China Mathematics》1989年第5期550-563,共14页中国科学：数学（英文版）

基　　金：Project supported by the National Natural Science Foundation of China.

摘　　要：<正> In this paper, a nontrivial counter example to Corduneanu and Lakshmikantham’s prob-lem is given on exponential stability of the fundamental matrix for a class of the mostfundamental autonomous linear functional differential equations with infinite retardations. Inabstract phase spaces, the necessary and sufficient conditions have been obtained for theexponential stability of the fundamental matrix of such general equations. It is shown thatsuch stability is independent of the selection of phase spaces and proved theoretically thatthe answer of Corduneanu and Lakshmikantham’s problem is false.In this paper, a nontrivial counter example to Corduneanu and Lakshmikantham’s prob-lem is given on exponential stability of the fundamental matrix for a class of the mostfundamental autonomous linear functional differential equations with infinite retardations. Inabstract phase spaces, the necessary and sufficient conditions have been obtained for theexponential stability of the fundamental matrix of such general equations. It is shown thatsuch stability is independent of the selection of phase spaces and proved theoretically thatthe answer of Corduneanu and Lakshmikantham’s problem is false.

关 键 词：FUNDAMENTAL matrix EXPONENTIAL stability functional differential equation. 

分 类 号：N[自然科学总论]