Asymptotic Integration of Nonautonomous Delay-Differential Systems

Abstract

We prove existence theorems and asymptotic formulas for the solutions of a class of delay-differential equations with time-state dependent lag. ᮊ 1996 Academic Press, Inc.

Asymptotically exponential solutions in nonlinear integral and differential equations

“…The study of asymptotic properties of different classes of integral and differential equations is an active research area, see, e.g., [6][7][8]12,14,15,17,[24][25][26]28] and the references therein. Most of the work in this direction has been done for linear equations, and guarantees only pure exponential growth/decay of the solutions.…”

Long-time behavior of positive solutions of a differential equation with state-dependent delay

“…Analyzing the assumptions of the results in [6,27] and comparing them with our investigation, we conclude the independency of the results obtained since assumptions (41), (42) are not included and are not necessary in the formulations of our results. Similarly, we can proceed when analyzing the assumptions in [20]. There exist many investigations concerned with differential equations with delays closely connected to the results of this paper.…”

“…in [20] where A(t) is a square matrix continuous on [0, ∞). Analyzing the assumptions of the results in [6,27] and comparing them with our investigation, we conclude the independency of the results obtained since assumptions (41), (42) are not included and are not necessary in the formulations of our results.…”

The Hartman–Wintner Theorem for Functional Differential Equations

“…In [3] Arino et al have obtained both types of results for the case when the unperturbed equation is a delay differential equation (B 0 {0, A 0 , B 0 are diagonal) assuming (1.15) with p=2 and some further conditions on A, B and the size of the delay. (For similar qualitative results for differential equations with state-dependent delay, see [8,12,20] and the references therein. )…”