Oscillation results for second-order neutral differential equations of mixed type

Abstract

ABSTRACT. Some oscillation theorems are established for the second-order linear neutral differential equations of mixed typeSeveral examples are also 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) = ∞.…”

On the oscillatory behavior of solutions of third order nonlinear neutral differential equations

“…Of late, a large amount of interest in oscillatory properties of various classes of third-order linear/nonlinear neutral differential equations has been found. Baculiková and Dzurina [2,3], Li et al [8,9] studied the oscillatory behavior of the second and third order differential equation if 0 ≤ p(t) < 1. Thandapani and Li [7] obtained oscillation results for Eq.…”

Second-Order Non-Canonical Neutral Differential Equations with Mixed Type: Oscillatory Behavior

“…Li [7] and Li et al [8] studied the oscillation of solutions of the second-order equation with constant mixed arguments:…”