Philos-Type Oscillation Results for Third-Order Differential Equation with Mixed Neutral Terms

Abstract

The motivation for this paper is to create new Philos-type oscillation criteria that are established for third-order mixed neutral differential equations with distributed deviating arguments. The key idea of our approach is to use the triple of the Riccati transformation techniques and the integral averaging technique. The established criteria improve, simplify and complement results that have been published recently in the literature. An example is also given to demonstrate the applicability of the obtained conditions.

Analysis on Controllability Results for Wellposedness of Impulsive Functional Abstract Second-Order Differential Equation with State-Dependent Delay

“…Next, we investigated the existence and uniqueness of the controllability of neutral impulsive differential equations with nonlocal conditions in prior work. The controllability of a nonlocal neutral impulsive differential equation under compactness conditions, Lipschitz conditions, and mixed-type conditions is obtained using the property of measure of noncompactness and Darbo-Sadovskii's fixed point theorem, read the cited papers [38,39]. We now extend our research to investigate the controllability and wellposedness of an impulsive functional abstract second order differential equation with state dependent delay.…”

On the Qualitative Behavior of Third-Order Differential Equations with a Neutral Term

“…Lately, great attention has been devoted to the theory of oscillation in DDEs. The works [12][13][14][15] develop techniques and methods for studying the oscillations of DDEs. This development was necessarily reflected in the study of the oscillation of third-order DDEs, and this can be seen through the works [16][17][18].…”

Oscillation and Asymptotic Properties of Differential Equations of Third-Order

“…However, to the best of our knowledge, only a few papers have studied the oscillation of nonlinear neutral delay differential equations of third order with distributed deviating arguments; see, for example, [2][3][4][5]. Recently, Haifei Xiang [6] and Haixia Wang et.…”