滞后型测度泛函微分方程解对参数的连续依赖性  

Continuous Dependence of Solution on Parameters for Retarded Measure Functional Differential Equation

作　　者：李宝麟 杨万秀 LI Bao-lin;YANG Wan-xiu(College of Mathematics and Statistics,Northwest Normal University,Lanzhou 730070)

机构地区：[1]西北师范大学数学与统计学院,兰州730070

出　　处：《工程数学学报》2021年第4期522-538,共17页Chinese Journal of Engineering Mathematics

基　　金：国家自然科学基金(11761063).

摘　　要：本文研究了保证滞后型测度泛函微分方程解对参数具有连续依赖性的充分条件.我们首先指出在一定条件下,所研究的滞后型测度泛函微分方程与一类广义常微分方程存在等价关系.随后将所研究的滞后型测度泛函微分方程转换为具有方便分析形式的广义常微分方程.再利用建立的广义常微分方程解对参数的连续依赖性结论,完成了滞后型测度泛函微分方程解对参数的连续依赖性定理.所获得的结果推广了相关文献的结论.In this paper,we study the sufficient conditions to guarantee the continuous dependence of the solution on parameters for retarded measure functional differential equation.We first point out an equivalent relationship between the retarded measure functional differential equation and a class of generalised ordinary differential equations under certain conditions.Then the delay measure functional differential equation is transformed into a generalised ordinary differential equation with a form convenient with analysing.Then,by using the conclusion of the continuous dependence of the solution of the generalised ordinary differential equation on the parameter,the continuous dependence theorem for the retarded measure functional differential equation is completed.The obtained results generalise the conclusions of the relevant literature.

关 键 词：滞后型测度泛函微分方程 连续依赖性 广义常微分方程 

分 类 号：O175.12[理学—数学]