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)=∑i=1mpix(t-τi)+f(t,x(t-σ1(t)),…,x(t-σn(t)))under a critical state by the second-order ordinary differential equation y″(t)+(1-ε)e-λ0tf(t,eλ0(t-σ1(t))y(t),…,eλ0(t-σn(t))y(t))=0.At the same time, necessary conditions for the above bounded oscillation equation are obtained.