ASYMPTOTIC AND OSCILLATORY BEHAVIOR OF SOLUTIONS OF 1ST ORDER NONLINEAR NEUTRAL DELAY DIFFERENTIAL-EQUATIONS

The authors consider the first order nonlinear neutral delay differential equation (E) [y(t) + P(t) y(t - τ)]′ - Q(t) f{hook}(y(t - σ)) = 0, where P, Q, and f{hook} are continuous, Q(t) ≧ 0, τ ≧ 0, σ ≧ 0, and uf{hook}(u) > 0 if u ≠ 0. They give sufficient conditions for all nonoscillatory solutions of (E) to converge to zero as t → ∞. Two oscillation theorems for equation (E) are also proved. © 1991.