Oscillatory Behavior of Second-Order Neutral Differential Equations

Abstract

In this paper, we study oscillatory properties of neutral differential equations. Moreover, we discuss some examples that show the effectiveness and the feasibility of the main results.

Weighted differential inequality and oscillatory properties of fourth order differential equations

“…This gives the left-hand estimate of (15). Moreover, from (29) we also deduce the left-hand estimate of (16).…”

“…Since the left-hand side of (19) does not depend on τ ∈ I, we find the right-hand estimate of (15). The function F(τ ) does not increase in τ ∈ I.…”

“…Therefore, the oscillatory properties of various models described by linear, quasilinear, and nonlinear differential equations, including delay differential equations, are intensely studied. Recently, [14,15], and [16] have investigated the oscillatory properties of second order impulsive differential equations, the research of which has been significantly developed in recent decades. Most of the results regarding the oscillatory properties of differential equations relate to second order equations.…”

A high order method for oscillatory delay differential equations

“…and presented oscillation conditions of (3). In [10], second-order nonlinear neutral differential equations (1) have been considered founding various oscillation criteria if equation (1) verifies the following hypotesys:…”

Sawi transform and Hyers-Ulam stability of n t h order linear differential equations

“…Singh [29] tackled the popular issue of development by fostering its numerical model as far as first order linear DE using ST. Gupta [3] introduced connection among Sawi and other essential transforms. The applications of differential equations in various fields, for example, the environment, financial matters, science and engineering can be displayed as [25][26][27][28][29][30][31][32]. Recently Viglialoro [10,15,30] investigated the properties of solutions to porous medium problems with different sources and boundary conditions, boundedness in a chemotaxis system with consumed chemoattractant and bounded solutions to a parabolic-elliptic chemotaxis system with nonlinear diffusion and signal-dependent sensitivity.…”