Necessary and Sufficient Conditions for Oscillation of Second Order Neutral Differential Equations

AbstractConsider the second order nonlinear neutral differential equation with delays: (E) d2/dt2[y(t)−py(t−τ)]+q(t)f(y(t−σ))=0, for t∈[0,∞), where q(t),f(x) are continuous functions, q(t)≥0, yf(y)>0 if y≠0, and 0<p<1, τ>0, σ>0. When f(y) satisfies either the superlinear or sublinear conditions which include the special case f(y)=y|y|γ−1 of γ>1 and 0<γ