During the last two decades, there has been much research activity concerning the oscillation and nonoscillation of solutions of neutral type delay differential equations see 1–9 . Investigation of such equations or systems, besides of their theoretical interest, have some importance in modelling of the networks containing lossless transmission lines, in the study of vibrating masses attached t...

We establish some new criteria for the oscillation of second-order Emden–Fowler neutral delay differential equations.We study the case of superlinear and the case of sublinear equations subject to various conditions. The results obtained show that the presence of a neutral term in a differential equation can cause or destroy oscillatory properties. Several examples are provided to illustrate th...

In this article, we obtain oscillation conditions for second-order differential equation with neutral term. Our results extend, improve, and simplify some known delay equations. Several effective illustrative implementations are provided.

In this paper we find sufficient conditions for every solution of the neutral delay difference equation ∆(rn∆(yn − pnyn−m)) + qnG(yn−k) = 0 to oscillate or to tend to zero or ±∞ as n → ∞, where ∆ is the forward difference operator given by ∆xn = xn+1−xn, pn, qn, and rn are infinite sequences of real numbers with qn ≥ 0, rn > 0. Different ranges of {pn} are considered. This paper improves,genera...