Nonlinear Variation of Constants Formula for Differential Equations with State-Dependent Delays

Research output: Contribution to journalArticle

2 Citations (Scopus)


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
Issue number3-4
Publication statusPublished - Sep 1 2016



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

ASJC Scopus subject areas

  • Analysis

Cite this