Oscillation of Second Order Nonlinear Neutral Differential Equations with Mixed Neutral Term

Abstract

In this paper, we obtained some sufficient conditions for the oscillation of all solutions of the second order neutral differential equation of the form t r t 0 d ∞ < ∞. Examples are provided to illustrate the main results.

On the oscillation of second-order half-linear functional differential equations with mixed neutral term

“…However, oscillation results for mixed neutral differential and dynamic equations are relatively scarce in the literature; some results can be found, for example, in [20][21][22][23][24][25][26][27][28][29][30][31][32], and the references cited therein. We would like to point out that the results obtained in [20][21][22][23][24][25][26][27][28][29][30][31][32] require both of p 1 and p 2 to be constants or bounded functions, and hence, the results established in these papers cannot be applied to the cases where lim t→∞ p 1 (t) = ∞ and /or lim t→∞ p 2 (t) = ∞. In view of the observations above, we wish to develop new sufficient conditions which can be applied to the cases where lim t→∞ p 1 (t) = ∞ and /or lim t→∞ p 2 (t) = ∞.…”