偶数阶连续分布变偏差泛函微分方程的振动性

OSCILLATORY BEHAVIORS OF EVEN ORDER FUNCTIONAL DIFFERENTIAL EQUATIONS WITH CONTINUOUS DISTRIBUTED DEVIATING ARGUMENTS

本文计论如下偶数阶泛函微分方程x^(2n)(t)-(?)p(t,ξ)x[g(t,ξ)]dσ(ξ)=0(n≥1,b>a) (1)x^(2n)(t)-(?)p(t,ξ)x[g(t,ξ)]dσ(ξ)=q(t)(n≥1,b>α) (2)解的振动性质.给出了(1)或(2)的一些振动性判别准则.这些准则是对 R.S.Dahiya 某些结果的推广.

In this paper we discuss the oscillatory behaviors for the follo- wing even order functional differential equations: x_-^(2n)(t)-(∫_a^bp(t,ζ)x[g(t,ζ)]dσ(ζ))=0(n≥1,b>a)(1) x^(2n)(t)-∫_a^bp(t,ζ)x[g(t,ζ)]dσ(ζ)=q(t)(n≥1,b>a).(2) Some oscillation criteria for(1)or(2)are given.These criteria are an extension of some results established by R.S.Dahiya.