时标上一类二维动力系统的非振荡解的存在性

Existence of Nonoscillatory Solutions of Two-Dimensional Time Scale Systems

时标理论的研究是将微分方程理论和差分方程理论有效的结合起来,且其结果比微分方程和差分方程理论应用更为广泛。本文通过Schauder不动点定理,Knaster不动点定理以及双重广义积分来证明时标上一类由一阶动力学方程构成的二维动力系统非振荡解的存在性问题,并通过一些实例来验证所得到的主要结果。

The study of time-scale theory combines the theory of differential equations with the theory of difference equations effectively, and the results obtained are more extensively used than those of differential equations and difference equations. In this paper, we employ Schauder’s fixed point theorem, Knaster’s fixed point theorem and double improper integrals to establish the existence of nonoscillatory solutions to the two-dimensional time scale system composed of first-order dynamic equations, and verify the main obtained results through some examples.