一类高阶拟线性中立型时滞微分方程解的振动性准则

Oscillation Criteria for Solutions of a Class of Higher Order Quasilinear Neutral Delay Differential Equations

主要研究了形如[r(t)ψ(u(t))|z(n-1)(t)|α-1 z(n-1)(t)]′+m∑i=1qi(t)fi(|u(τi(t))|αi-1u(τi(t)))=0,t≥t0的一类高阶拟线性中立型时滞微分方程在条件∫∞t0r1/α(s)ds=∞或∫∞t0r1/α(s)ds<∞下的振动性.推广和改进了已有的结论.

This paper mainly studies the oscillation of a class of high order quasilinear neutral delay differential equation of the form[r(t)ψ(u(t))|z^(n-1)(t)|α-1z(n-1)(t)]′+∑i=1^mqi(t)fi(|u(τi(t))|^αi-1u(τi(t)))=0,t≥t0 under the condition∫t0^∞r1/α(s)ds=∞to∫t0^∞r1/α(s)ds<∞.The results of this paper generalize and improve some of the existing conclusions.