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Oscillation of impulsive delay differential equations and applications to population dynamics

Published online by Cambridge University Press:  17 February 2009

Jurang Yan ,
Aimin Zhao  and
Linping Peng
Jurang Yan
Affiliation:
School of Mathematical Sciences, Shanxi University, Taiyuan, Shanxi 030006, People's Republic of China; e-mail: jryan@sxu.edu.cn.
Aimin Zhao
Affiliation:
School of Mathematical Sciences, Shanxi University, Taiyuan, Shanxi 030006, People's Republic of China; e-mail: jryan@sxu.edu.cn.
Linping Peng
Affiliation:
School of Science, Beijing University of Aeronautics and Astronautics, Beijing 100083, People's Republic of China.
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Abstract

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The main result of this paper is that the oscillation and nonoscillation properties of a nonlinear impulsive delay differential equation are equivalent respectively to the oscillation and nonoscillation of a corresponding nonlinear delay differential equation without impulse effects. An explicit necessary and sufficient condition for the oscillation of a nonlinear impulsive delay differential equation is obtained.

Type
Research Article
Information
The ANZIAM Journal , Volume 46 , Issue 4 , April 2005 , pp. 545 - 554
Copyright
Copyright © Australian Mathematical Society 2005

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