On the asymptotic behavior of solutions of some delay differential systems which have a first integral
type: Item
instance of: scholarly article
title: On the asymptotic behavior of solutions of some delay differential systems which have a first integral
zbMATH Open document ID: 0614.34063
DOI: 10.1016/0022-247X(87)90342-8
author: Ovide Arino
author: E. Haourigui
published in: Journal of Mathematical Analysis and Applications
publication date: 1987-01-01T00:00:00Z
review text: This paper extends a previous publication by the first author and \textit{P. Seguier} [ibid. 96, 420-436 (1983; Zbl 0527.34066)] who considered asymptotic behaviour of the solutions of scalar nonautonomous delay differential equations which have a first integral. Earlier examples of that kind were introduced by K. L. Cooke and J. Yorke in the study of epidemiological problems. These are autonomous equations \(dx/dt=g(x(t))- g(x(t-T)).\) The most general (and elegant) result about asymptotic behaviour of such equations appeared in 1978 in a joint paper by J. Kaplan, M. Sorg and J. Yorke. Other related results were obtained, notably by J. Haddock, T. Krisztin and by C. Jehu who indirectly inspired the present work. While the work with P. Seguier mainly uses comparison results due to monotonicity with respect to the delay terms, the main tool here is a Lyapunov functional on the pairs of solutions, coupled with a first integral. For systems, the main field of applications is compartmental analysis and, indeed, the class of systems under consideration here is a non-autonomous version of a compartmental model originally derived by I. Gyori. Partial asymptotic results (for example, not considering periodic dependence) were previously obtained by I. Gyori.
Mathematics Subject Classification ID: 34K99
Mathematics Subject Classification ID: 92D25
zbMATH DE Number: 3994068
zbMATH Keywords: scalar nonautonomous delay differential equations
zbMATH Keywords: epidemiological problems
MaRDI profile type: Publication
cites work: Exponential dichotomy and existence of pseudo almost-periodic solutions of some differential equations
cites work: About the behaviour at infinity of solutions of \(x'(t)=f(t-1,x(t-1))-f(t,x(t))\).
cites work: Connections between compartmental systems with pipes and integro-differential equations
cites work: Compartmental systems with pipes
cites work: Q3687210
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description: scientific article; zbMATH DE number 3994068