Asymptotic theory for a class of nonautonomous delay differential equations

J. R. Haddock, Yang Kuang

Research output: Contribution to journalArticle

13 Citations (Scopus)

Abstract

This paper deals with asymptotic behavior of solutions of the nonlinear nonautonomous delay differential equation x′(t) = -∝t - r(t) t f(t, x(s))dμ(t, s), (su*) where xf(t, x) ≥ 0, f(t, 0) = 0, t - r(t) nondecreasing, μ(t, s) is nondecreasing and of bounded variation. General sufficient conditions, which are easy to verify, are obtained for the solutions to be bounded and asymptotically stable (locally and globally). These results improve many existing ones principally by allowing: (i) r(t) to be unbounded, (ii) both discrete and distributed delays, and (iii) the equation to be strongly nonlinear and nonautonomous. Various examples are given in the form of corollaries with a highly flexible integrand.

Original languageEnglish (US)
Pages (from-to)147-162
Number of pages16
JournalJournal of Mathematical Analysis and Applications
Volume168
Issue number1
DOIs
StatePublished - Jul 15 1992

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Nonautonomous Differential Equations
Asymptotic Theory
Delay Differential Equations
Differential equations
Discrete Delay
Distributed Delay
Bounded variation
Asymptotic Behavior of Solutions
Integrand
Asymptotically Stable
Corollary
Verify
Sufficient Conditions
Class
Form

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

Cite this

Asymptotic theory for a class of nonautonomous delay differential equations. / Haddock, J. R.; Kuang, Yang.

In: Journal of Mathematical Analysis and Applications, Vol. 168, No. 1, 15.07.1992, p. 147-162.

Research output: Contribution to journalArticle

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