时间测度链上一类二阶非线性中立型泛函动态方程的振荡性

Oscillation for certain second-order nonlinear neutral functional dynamic equations on time scales

为了进一步发展和完善时间测度链上动态方程的振荡理论,讨论了时间测度链上一类二阶非线性中立型变时滞动态方程{a(t)φ1([x(t)+p(t)x(τ(t))]Δ)}Δ+q(t)f(φ2(x(δ(t))))=0的振荡性,这里φ1(u)=uα-1 u,φ2(u)=uβ-1 u(α>0,β>0均为实常数),得到了该方程振荡的新准则,并举例说明了定理的应用.

In order to develop and improve the theory about oscillation of dynamic equations on time scales , this paper is concerned with oscillations of certain second‐order nonlinear neutral variable delay dynamic equation{a（t）φ1 （[x（t）＋ p（t）x（τ（t））]Δ）}Δ ＋ q（t） f （φ2 （x（δ（t））））=0 on a time scale T , where φ1 （u）=u α-1 u ,φ2 （u）= u β-1 u ,α〉 0 ,β〉 0 are constants . A new oscillation criteria is established for the equation . An example is given to illustrate the result .