Differentiability of Solutions with Respect to the Initial Data in Differential Equations with State-dependent Delays

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Abstract

In this paper we consider a class of differential equations with state-dependent delays. We show differentiability of the solution with respect to the initial function and the initial time for each fixed time value assuming that the state-dependent time lag function is strictly monotone increasing.

Original languageEnglish
Pages (from-to)843-884
Number of pages42
JournalJournal of Dynamics and Differential Equations
Volume23
Issue number4
DOIs
Publication statusPublished - Dec 1 2011

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Keywords

  • Delay differential equation
  • Differentiability with respect to parameters
  • State-dependent delay

ASJC Scopus subject areas

  • Analysis

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