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

Abstract

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