Oscillation of impulsive delay differential equations and applications to population dynamics

ANZIAM J. 46 (2005), 545-554

Oscillation of impulsive delay differential equations and applications to population dynamics

Jurang Yan
School of Mathematical Sciences
Shanxi University
Taiyuan
Shanxi 030006
People's Republic of China
jryan@sxu.edu.cn

Aimin Zhao
School of Mathematical Sciences
Shanxi University
Taiyuan
Shanxi 030006
People's Republic of China

and

Linping Peng
School of Science
Beijing University of Aeronautics and Astronautics
Beijing 100083
People's Republic of China

Abstract

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.

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