中北大学学报（自然科学版）2012，Vol.33Issue(1)：36-39,4.DOI:10.3969/j.issn.1673-3193.2012.01.010
具有状态依赖时滞的微分方程初值问题的解
Solutions to State-Dependent Delay Differential Equations with Initial Value Conditions
邓瑞娜 1赵爱民1
作者信息
- 1. 山西大学数学科学学院,山西太原030006
- 折叠
摘要
Abstract
The functional differential equation with state-dependent delay x' (t)=f(t,x(t-r(x,))) , was considered and the basic properties of its solution that satisfying the initial conditions xn = f, in which /.[0,oo) XR-*R, p6C. Was studied by using the method of steps. By constructing the iterative sequence, the existence of unique solution of this equation with initial value conditions in the interval [-h,oo) was obtained, and it was Lipschitz continuous. The above work extends the corresponding results from H. O. Walther.关键词
状态依赖时滞/泛函微分方程/步法/Lipschitz连续Key words
state^dependent delay/ functional differential equation/ method of steps/ Lipschitz continuous分类
数理科学引用本文复制引用
邓瑞娜,赵爱民..具有状态依赖时滞的微分方程初值问题的解[J].中北大学学报（自然科学版）,2012,33(1):36-39,4.
