﻿ 一类三阶中立型半线性时滞微分方程振动准则 Oscillate Criteria of Third Order Semi-Linear Neutral Differential Equations with Delay Argument

Pure Mathematics
Vol.07 No.04(2017), Article ID:21475,7 pages
10.12677/PM.2017.74045

Oscillate Criteria of Third Order Semi-Linear Neutral Differential Equations with Delay Argument

Quandi Li, Ju Yang, Xiaoxian Li, Quanwen Lin*

Department of Mathematics, Science of School, Guangdong University of Petrochemical Technology, Maoming Guangdong

Received: Jul. 4th, 2017; accepted: Jul. 19th, 2017; published: Jul. 25th, 2017

ABSTRACT

We study the oscillatory of third order semi-linear neutral differential equations with delay argument. Using a generalized Riccati substitution and inequation technique, and consulting some results in recent literature, a new oscillation criterion is established and proved, also a number of examples are given to prove their efficiency.

Keywords:Oscillation Criterion, Third Order Semi-Linear Neutral Differential Equations with Delay Argument, Generalized Riccati Substitution

1. 引言

(E)

(I)

(II)

2. 主要结果

(2.1)

(2.2)

,

, , , ,

(I) 假设

，则有

, (2.3)

(2.4)

(2.5)

(2.6)

(2.7)

(II) 假设

(2.8)

(2.9)

(2.10)

(2.11)

(2.12)

，得

(2.13)

(2.14)

(2.15)

(2.16)

3. 例子

, (3.1)

,

,

,

，式(3.1)满足定理2.1，故方程(3.1)是振动。

Oscillate Criteria of Third Order Semi-Linear Neutral Differential Equations with Delay Argument[J]. 理论数学, 2017, 07(04): 356-362. http://dx.doi.org/10.12677/PM.2017.74045

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