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

Comparison Theorems on the Oscillation and Asymptotic Behaviour of Higher-Order Neutral Differential Equations

“…For odd-order delay differential equations, the readers may find very interesting results in the papers [2, 4, 5, 8, 20, 27], and we wish to point out here that all these mentioned papers study (1) with (R2). To the best of our knowledge, [6,[15][16][17][18][19] are the only papers including some results for (1) for arbitrary-order neutral delay differential equations. Since the conditions in the papers mentioned above are different from ours, our technique is completely different, and it is indeed interesting to point out that our results are not directly comparable with their results.…”

Oscillatory and asymptotic behaviour of a nonlinear second order neutral differential equation

“…It is well known that behaviour of solutions of odd order and even order NDDEs are quite different at times. In [1], [2], [5], [8], [9] the authors have studied the behaviour of solutions of NDDEs of second order. It seems that [8] is the only result about the oscillatory behaviour of solutions of second order neutral equation (E), available in the literature.…”

“…In [8] and [9] only one range of p(t) is considered and the results there hold for G satisfying either (4) or (9). In this paper an attempt is made to extend p(t) to all possible ranges.…”

“…Even the conditions assumed by different authors for similar type of equations are often not comparable. Because of the simplicity of the hypothesis assumed in this paper we ask for a comparison of our result with some of the work of [2] and [9]. While considering p(t) in a particular range we tried to give two results one with (H 4 ) and another with (H 5 ).…”

Non-oscillatory criteria for a class of second order non-linear forced neutral-delay differential equations

“…We observe that the even order neutral differential equations are not so often studied as the odd order neutral differential equations have been. The authors have proved the existence of a bounded positive solution of neutral delay differential equations of various order in [1], [2], [5], [6], [7], [8], [9]. For that the authors assume the following hypothesis.…”