具有振动系数的二阶非线性中立型时滞动力方程的有界振动性

摘要/Abstract

摘要：

研究时标T上具有振动系数的二阶非线性中立型时滞动力方程
(r(t)([y(t)+p(t)y(τ(t))]^Δ)^α)^Δ+f(t, y(δ(t)))=0
的有界振动性, 其中p是一个定义于T上的振动函数, α>0是两个正奇数之比. 利用一种Riccati变换技术, 获得了该方程所有有界解振动的几个充分条件, 推广和补充了文献中要求p(t)≥0的一些结果, 并举例说明了该文主要结果的应用.

关键词: 有界振动性, 二阶非线性中立型时滞动力方程, 振动系数, 时标, Riccati变换

Abstract:

In this paper, we investigate the oscillation of bounded solutions of second-order nonlinear neutral delay dynamic equation with oscillating coefficients of the form
(r(t)([y(t)+p(t)y(τ(t))]^Δ)^α)^Δ+f(t, y(δ(t)))=0
on an arbitrary time scale T, where p is an oscillating function defined on T and α>0 is a quotient of odd positive integers. We get some sufficient conditions for the oscillation of all bounded solutions of the equation by developing a Riccati transformation technique. The obtained results extend and complement some known results in which p(t)≥0 for t∈T is required. Several examples are presented to illustrate our main results.

Key words: Bounded oscillation, Second-order nonlinear neutral delay dynamic equation, Oscillating coefficient, Time scale, Riccati transformation

中图分类号:

39A10

陈大学. 具有振动系数的二阶非线性中立型时滞动力方程的有界振动性[J]. 数学物理学报, 2013, 33(1): 98-113.

CHEN Da-Xue. Bounded Oscillation for Second-order Nonlinear Neutral Delay Dynamic Equations with Oscillating Coefficients[J]. Acta mathematica scientia,Series A, 2013, 33(1): 98-113.

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