Asymptotic theory for a class of nonautonomous delay differential equations

J. R. Haddock, Yang Kuang

Research output: Contribution to journalArticle

14 Scopus citations

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

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

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