具正负系数的二阶差分方程的振动性

J4 ›› 2011, Vol. 46 ›› Issue (8): 59-62.

具正负系数的二阶差分方程的振动性

杨甲山, 孙文兵

邵阳学院理学与信息科学系, 湖南邵阳 422004

收稿日期:2010-10-05 出版日期:2011-08-20 发布日期:2011-09-08
作者简介:杨甲山(1963- ),男, 副教授, 研究方向为微分差分方程. Email:syxyyjs@163.com
基金资助:
湖南省教育厅科研重点资助项目(09A082)

Oscillation of second order difference equations with positive and negative coefficients

YANG Jia-shan, SUN Wen-bing

Department of Science and Information, Shaoyang University, Shaoyang 422004, Hunan, China

Received:2010-10-05 Online:2011-08-20 Published:2011-09-08

摘要/Abstract

摘要：

研究了一类具有正负系数的二阶非线性中立型变时滞差分方程的振动性。利用Banach空间的不动点原理, 引入参数函数和Riccati变换, 获得了该类方程存在非振动解的新准则, 同时得到了该类方程振动的判别准则, 这些准则改善了方程的条件限制, 所得结论推广并改进了现有文献中的结果。

关键词: 正负系数; 中立型差分方程; 变时滞; 非线性; 振动和非振动; Riccati变换

Abstract:

The oscillation of a class of second order nonlinear neutral variable delay difference equation with positive and negative coefficients is discussed. Using the fixed point theorem in Banach space, a new nonoscillation criteria for the equation is obtained by introducing parameter function and the generalized Riccati transformation. Also, a sufficient condition for oscillation of the equation is proposed. These criteria can improve the restriction of the conditions for the equation, which promote some existed results.

Key words: positive and negative coefficient; neutral difference equation; variable delay; nonlinear; oscillation and nonoscillation; Riccati transformation

杨甲山, 孙文兵. 具正负系数的二阶差分方程的振动性[J]. J4, 2011, 46(8): 59-62.

YANG Jia-shan, SUN Wen-bing. Oscillation of second order difference equations with positive and negative coefficients[J]. J4, 2011, 46(8): 59-62.

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