﻿ 一类高阶线性泛函方程的振动准则 Oscillate Criteria of a Class of Higher Order Linear Functional Equations

Pure Mathematics
Vol.07 No.03(2017), Article ID:20670,12 pages
10.12677/PM.2017.73026

Oscillate Criteria of a Class of Higher Order Linear Functional Equations

Lina Dai, Simin Wu*, Quanwen Lin, Xinxiao Su

Science College, Guangdong University of Petrochemical Technology, Maoming Guangdong

Received: May. 6th, 2017; accepted: May 21st, 2017; published: May 25th, 2017

ABSTRACT

This paper mainly studies oscillatory of a class of higher order linear functional equations of the form, where are given real valued functions and. Some sufficient conditions for the oscillation of all solutions of this equation are obtained. And our results generalize and improve some results in some literature given.

Keywords:Oscillation, High Order, Linear, Functional Equations

1. 引言

(1.1)

(1.2)

(1.3)

(1.4)

(1.5)

1995年，Nowakowska和Werbowsk [2] ：将条件(1.4)推广到方程

(1.6)

(1.7)

(1.8)

1999年，周勇和俞元洪 [3] 研究方程(1.1)的解的振动性。他们证明了方程(1.1)的所有解振动，如果

(1.9)

(1.10)

2. 主要定理及相关证明

(2.1)

(2.2)

，对任意，有

(2.3)

，即

(2.4)

(2.5)

，得到(2.1)即有

(2.6)

(2.7)

(2.8)

(2.9)

(2.10)

(2.11)

(2.12)

(2.13)

(2.14)

。证毕

(2.15)

(2.16)

(2.17)

(2.18)

(2.19)

(2.20)

(2.21)

(2.22)

(2.23)

(2.24)

Oscillate Criteria of a Class of Higher Order Linear Functional Equations[J]. 理论数学, 2017, 07(03): 200-211. http://dx.doi.org/10.12677/PM.2017.73026

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16. NOTES

*通讯作者。