Bounded oscillation for second order non-linear neutral delay differential equations in critical and non-critical cases

Sufficient and necessary conditions for the bounded oscillation of the second order non-linear neutral delay differential equation[x(t)-px(t-τ)]″=∑i=1mqix(t-σi)+f(t,x(t-η1(t)),…,x(t-ηn(t)))are obtained in critical and non-critical cases.