方程[x(t)+p(t)x(t-r)]′+(sum from i=1 to n)q_i(t)×x(t-r_i)=0的振动性

OSCILLATIONS OF THE NEUTRAL DIFFERENTIAL EQUATION [x(t)+p(t)x(t-r)]'+sum from i=1 to nqi(t)x(t-ri)=0

在方程[x(t)+p(t)x(t-r)]′+sum from i=1 to n qi(t)x(t-ri)=0中,p(t)、qi(t)(i=1,2,…,n)是t的连续函数对0≤p(t)≤A<+∞,-1≤p(t)≤A<0,-∞<B≤p(t)≤A<-1的3种情形,给出此方程一切解振动的判别准则。

In this paper, we consider the behavior of the solutions of nonlinear differential equation y^((n))=f(t, y). (1) We give some conditions wich guarentee that the solution y(t) of (1) satisfies lira [y(t)-p(t)]=0, where p(t) is a polynomial t→+∞ of degree≤(n-1), and under the same conditions, for each polynomial p(t) of degree≤(n-1), there exists a solution y(t) of (1) such that lim [y(t)-p(t)]=0. Our results in this paper t→+∞ eontain the related theorems in [1]、[2]、[3] as special cases.