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

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(r(t))]△)α)△+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.

Bounded Oscillation for Second-order Nonlinear Neutral Delay Dynamic Equations with Oscillating Coefficients

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)))=0on 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.