具连续变量的二阶超线性中立型差分方程的有界振动性

The Bounded Oscillatory Behavior of a Class of Second Order Superlinear Neutral Difference Equations with Continuous Arguments

由于计算机科学、生物学、控制理论、医学及经济学等自然科学和边缘学科的进一步发展,提出了许多由差分方程描述的具体数学模型,因而对差分方程的研究在理论和实际应用二方面都具有重要意义。本文利用Banach压缩映射原理和一些分析技巧,研究了一类具有连续变量的不稳定型二阶超线性中立型时滞差分方程无界正解的存在性和有界解振动性问题,得出了该类方程无界正解的存在性定理及有界解振动的一个充分条件。

With the development of natural science and interdisciplinary subjects such as computer science, biology, control theory, medicine, and economics, many mathematical models need to be described by difference equations, therefore, the study of difference equations is of significance in both theory and practical application. In this paper, a class of second order unstable neutral difference equations with continuous arguments are investigated. By using Banach contractive operator theory and some necessary analysis techniques, the existence of the unbounded positive solutions and the oscillation of the bounded positive solutions are shown. Moreover a sufficient condition about them is given.