Oscillatory Properties of Third-Order Neutral Delay Differential Equations with Noncanonical Operators

Abstract

In the paper, we study the oscillatory and asymptotic properties of solutions to a class of third-order linear neutral delay differential equations with noncanonical operators. Via the application of comparison principles with associated first and second-order delay differential inequalities, we offer new criteria for the oscillation of all solutions to a given differential equation. Our technique essentially simplifies the process of investigation and reduces the number of conditions required in previously known results. The strength of the newly obtained results is illustrated on the Euler type equations.

Oscillation and Asymptotic Behavior of a Three-Dimensional Half-Linear System of Third-Order of Neutral Type

“…In recent years, the theory of neutral differential equations has become an independent area of research. Investigation of the oscillation and non-oscillation of neutral differential equations had already been initiated in the sixties and became popular in the eighties [3][4][5][6][7][8][9][10][11]. A few of them have been investigated in the system of neutral differential equations [12][13][14].…”

Almost Oscillatory Solutions of a Three-Dimensional Half-Linear Neutral differential System of the Second Order

“…NDEs represent one of these equations that have been of interest to many researchers, especially in the subject of oscillation and the behavior of the solution (see [4][5][6][7][8]). The oscillation properties of systems of differential equations, whether they are ordinary, delay, neutral, difference equations, or dynamic equations is the main concern of study (see [9][10]). A few of these oscillation properties have been investigated in the system of NDEs, (see [11][12][13]).…”

On the Oscillation of Solutions of Differential Equations with Neutral Term

“…Xing et al [9] and Moaaz et al [10] also extended this evolution to differential equations of the neutral type. Therefore, there are many studies on the oscillatory and asymptotic behavior of different orders of some differential equations, see [11][12][13][14][15][16][17][18][19][20][21][22][23][24][25].…”