Nonlinear Variation of Constants Formula for 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 piecewise monotone increasing. Based on these results, we prove a nonlinear variation of constants formula for differential equations with state-dependent delay. As an application, we discuss asymptotic properties of perturbed nonlinear differential equations with state-dependent delays.

Original languageEnglish
Pages (from-to)1187-1213
Number of pages27
JournalJournal of Dynamics and Differential Equations
Volume28
Issue number3-4
DOIs
Publication statusPublished - Sep 1 2016

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Keywords

  • Delay differential equation
  • Differentiability with respect to parameters
  • Nonlinear variation of constants formula
  • State-dependent delay

ASJC Scopus subject areas

  • Analysis

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