Asymptotics of delay differential equations via polynomials

Article type: Research Article

Authors: Wang, Xiang-Sheng

Affiliations: Department of Mathematics, Southeast Missouri State University, Cape Girardeau, MO 63701, USA. E-mail: xswang@semo.edu

Abstract: In this paper, we introduce an innovative and systematic technique to study delay differential equations via polynomials. First, we review an intrinsic relation between delay differential equations and polynomials. From this relation, we obtain long time behaviors of the solutions to delay differential equations via asymptotic analysis of the corresponding polynomials. Moreover, we derive asymptotic formulas and upper bounds for the intrinsic growth rate of delay differential equations, as well as a Gronwall-type inequality for delay differential inequalities.

Keywords: delay differential equations, asymptotic analysis, Gronwall-type inequality, intrinsic growth rate

DOI: 10.3233/ASY-141232

Journal: Asymptotic Analysis, vol. 90, no. 1-2, pp. 83-103, 2014