On Oscillation of Solutions of Forced Nonlinear Neutral Differential Equations of Higher Order

In this paper, necessary and sufficient conditions are obtained for every bounded solution of

$$left( * right)quad quad quad quad quad quad left[ {yleft( t right) - pleft( t right)yleft( {t - tau } right)^{left( n right)} } right] + Qleft( t right)Gleft( {yleft( {t - sigma } right)} right) = fleft( t right),quad t geqslant 0,$$

to oscillate or tend to zero as t → ∞ for different ranges of p(t). It is shown, under some stronger conditions, that every solution of (*) oscillates or tends to zero as t → ∞. Our results hold for linear, a class of superlinear and other nonlinear equations and answer a conjecture by Ladas and Sficas, Austral. Math. Soc. Ser. B 27 (1986), 502–511, and generalize some known results.