Abstract
In this paper, a kind of half-linear impulsive delay differential equations with damping is studied. By employing a generalized Riccati technique and the impulsive differential inequality, we derive several oscillation criteria which are either new or improve several recent results in the literature. In addition, we provide several examples to illustrate the use of our results.
Highlights
1 Introduction Impulsive differential equations are used to simulate processes and phenomena observed in control theory, physics, chemistry, population dynamics, biotechnologies, industrial robotics, etc., and their qualitative properties are important
In [ ], Chen and Feng showed a few examples and indicated that some of the oscillations did favor the stability of system, but some might destroy the balance of the system
Some scholars have been attracted by the problems of the oscillations of higher order differential equations and higher order impulsive differential equations and made relative advances therein in [ – ]
Summary
Impulsive differential equations are used to simulate processes and phenomena observed in control theory, physics, chemistry, population dynamics, biotechnologies, industrial robotics, etc., and their qualitative properties are important. In [ – ], the delay effect to impulsive equations is considered and some interesting results of oscillations are obtained. He obtained sufficient conditions which guaranteed the oscillation of every solution of ( ).
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