非线性非自治差分系统的振动性

Oscillations of Nonlinear Nonautonomous Difference Systems

本文建立非线性非自治差分系统及非线性非自治具分段常数变元的系统ｆ－－０所有解为振动的判别准则，其中［·］表示最大整数函数，Ａｒ为ｋ×ｋ矩阵值函数，而Ｆｒ为连续的ｋ维向量值函数。作为所得结果的应用，还给出了一些例子。

Consider the nonlinear nonautonomous difference systems of the form: and the nonlinear nonautonomous systems with piecewise constant argument of the form: Where [.] denotes the greatest integer function, Ar is a k×k matrix-valued function,and F is a continuous k-dimensional vector-valued function. Criteria for ascillations of all solutions of both systems are established. As applications of the obtained results, several examples are also given.