Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
9509644 | Journal of Computational and Applied Mathematics | 2005 | 12 Pages |
Abstract
In this paper we shall consider the following nonlinear impulsive delay differential equation xâ²(t)+αV(t)x(t)xn(tâmÏ)θn+xn(tâmÏ)=λ(t),a.e.t>0,tâ tk,x(tk+)=1(1+bk)x(tk),k=1,2,â¦,where m and n are positive integers, V(t) and λ(t) are positive periodic continuous functions with period Ï>0. In the nondelay case (m=0), we show that the above equation has a unique positive periodic solution xâ(t) which is globally asymptotically stable. In the delay case, we present sufficient conditions for the global attractivity of xâ(t). Our results imply that under the appropriate periodic impulsive perturbations, the impulsive delay equation shown above preserves the original periodic property of the nonimpulsive delay equation. In particular, our work extends and improves some known results.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Applied Mathematics
Authors
Wan-Tong Li, Hai-Feng Huo,