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

doi:10.1007/s11464-010-0005-9

Front. Math. China

2010, Vol. 5

Issue (2): 221-286 https://doi.org/10.1007/s11464-010-0005-9

Research articles

本期目录

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

Yuming CHEN¹,Qingwen HU²,Jianhong WU³,

1.Department of Mathematics, Wilfrid Laurier University, Waterloo, ON N2L 3C5, Canada; 2.Department of Mathematics and Statistics, Memorial University of Newfoundland, St. John’s, NL A1C 5S7, Canada; 3.Department of Mathematics and Statistics, York University, Toronto, ON M3J 1P3, Canada;

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Abstract：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 W¹,p-norm (1≤p<∞).

Key words： Delay differential equation adaptive delay differentiability of solution state-dependent delay uniform contraction principle locally complete triple-normed linear space

出版日期: 2010-06-05

引用本文:

. Second-order differentiability with respect to parameters for differential equations with adaptive delays[J]. Front. Math. China, 2010, 5(2): 221-286.
Yuming CHEN, Qingwen HU, Jianhong WU, . Second-order differentiability with respect to parameters for differential equations with adaptive delays. Front. Math. China, 2010, 5(2): 221-286.

链接本文:

https://academic.hep.com.cn/fmc/CN/10.1007/s11464-010-0005-9
https://academic.hep.com.cn/fmc/CN/Y2010/V5/I2/221

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