Second-order differentiability with respect to parameters for differential equations with adaptive delays

被引：9
|
作者：
Chen, Yuming [2 ]
Hu, Qingwen [3 ]
Wu, Jianhong [1 ]
机构：
[1] York Univ, Dept Math & Stat, N York, ON M3J 1P3, Canada
[2] Wilfrid Laurier Univ, Dept Math, Waterloo, ON N2L 3C5, Canada
[3] Mem Univ Newfoundland, Dept Math & Stat, St John, NF A1C 5S7, Canada
来源：
FRONTIERS OF MATHEMATICS IN CHINA | 2010年 / 5卷 / 02期
关键词：
Delay differential equation; adaptive delay; differentiability of solution; state-dependent delay; uniform contraction principle; locally complete triple-normed linear space; STATE-DEPENDENT DELAY; STRUCTURED POPULATION-GROWTH; PERIODIC-SOLUTIONS; TIME-DELAY; MODEL; STAGE; EXISTENCE;
D O I：
10.1007/s11464-010-0005-9
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
In this paper, we study the second-order differentiability of solutions with respect to parameters in a class of delay differential equations, where the evolution of the delay is governed explicitly by a differential equation involving the state variable and the parameters. We introduce the notion of locally complete triple-normed linear space and obtain an extension of the well-known uniform contraction principle in such spaces. We then apply this extended principle and obtain the second-order differentiability of solutions with respect to parameters in the W (1,p) -norm (1 a (c) 1/2 p < a).
引用
收藏
页码：221 / 286
页数：66
相关论文
共 50 条
12345