n阶线性脉冲微分方程解的振动性

Oscillations of N-order Linear Differential Equation with Impulses

脉冲微分方程解的振动性由于在物理、生态、工程等领域有其应用背景,引起了人们的广泛兴趣,正在成为研究的热点．本文讨论了一类n阶线性脉冲微分方程解的振动性和非振动性,分别给出了n为奇数和偶数时该方程振动和非振动的充分条件,并通过3个例题说明了文中定理的应用,所得结论改进并推广了部分文献的相关结果．

Oscillations of solutions for impulsive differential equations are of very important realistic significance in physics, biology, engineering, etc., which has been focused on and deeply investigated by many authors. In this paper, oscillations and non-oscillations of solutions for n-order, n be odd or even, linear differential equation with impulses are considered and some sufficient conditions for oscillations and non-oscillations of solutions are obtained, which improve and popularize some results in parts of the relative references. Finally, the results are illustrated with three examples.