Initial value problems for nonlinear nonresonant delay differential equations with possibly infinite delay

Lance D. Drager, William Layton

Research output: Contribution to journalArticle

1 Scopus citations

Abstract

We study initial value problems for scalar, nonlinear, delay differential equations with distributed, possibly infinite, delays. We consider the initial value problem (Equation presented), where ψ and f are bounded and μ is a finite Borel measure. Motivated by the nonresonance condition for the linear case and previous work of the authors, we introduce conditions on g. Under these conditions, we prove an existence and uniqueness theorem. We show that under the same conditions, the solutions are globally asymptotically stable and, if μ satisfies an exponential decay condition, globally exponentially asymptotically stable.

Original languageEnglish
Pages (from-to)1-20
Number of pages20
JournalElectronic Journal of Differential Equations
Volume1997
StatePublished - Dec 19 1997

Keywords

  • Asymptotic stability
  • Delay differential equation
  • Exponential asymptotic stability
  • Infinite delay
  • Initial value problem
  • Nonresonance

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