时间轴上一类二阶动态系统振荡的充分条件

Sufficient conditions of oscillation for certain second-order dynamic equations on time scales

研究时间轴T上的一类具非线性中立项的非线性的二阶中立型变时滞动态系统[A(t)ф(yΔ(t))]Δ+∑mi=1Pi(t)fi(ф(x(δi(t))))=0的振荡性,这里y(t)=x(t)+∑lj=1Bj(t)gj(x(τj(t)))且ф(u)=|u|λ-1 u(λ>0为实常数),得到了该动态系统振荡的几个新的充分条件,并举例说明了论文定理的应用.

This paper studied oscillations of the second-order nonlinear neutral variable delay dynamic equation [A（t）φ（yΔ（t））]Δ＋∑mi=1Pi（t）fi（φ（x（δj（t）））） =0 with nonlinear neutral on a time scaleT,wherey（t） =x（t）＋∑Bj（t）gj（x（τj（t））） and φ（u）=｜u｜λ-1u（here,λ＞0 is a constant）.We established some new sufficient conditions for this equation.Some examples were given to illustrate the main results.