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.
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.
出处
《数学物理学报（A辑）》
CSCD
北大核心
2013年第1期98-113,共16页
Acta Mathematica Scientia
基金
湖南省自然科学基金(11JJ3010)资助
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
Bounded oscillation
Second-order nonlinear neutral delay dynamic equation
Oscillating coefficient
Time scale
Riccati transformation.
