Bounded oscillation for second-order nonlinear delay differential equation in a critical state

In this paper we establish sufficient conditions for bounded oscillation of the second-order nonlinear delay differential equation x''(t) = Sigma(m)(i=1)pix(t - tau(i)) + f(t,x(t - sigma(1)(t)),...,x(t - sigma(n)(t))) under a critical state by the second-order ordinary differential equation y''(t) + (1 - epsilon)e(-gimel 0t) f(t,e(gimel 0(t - sigma 1(t)))y(t),...,e(gimel 0(t - sigma n(t)))y(t)) = 0. At the same time, necessary conditions for the above bounded oscillation equation are obtained. (c) 2005 Elsevier B.V. All rights reserved.