[1]周效良,王五生.高阶拟线性变时滞差分方程正解的存在性[J].四川师范大学学报(自然科学版),2010,(06):760.
 ZHOU Xiao liang,WANG Wu sheng.Existence of Positive Solutions of Higher Order QuasilinearDifference Equations with Variable Delay[J].Journal of SichuanNormal University,2010,(06):760.
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高阶拟线性变时滞差分方程正解的存在性()
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《四川师范大学学报(自然科学版)》[ISSN:1001-8395/CN:51-1295/N]

卷:
期数:
2010年06期
页码:
760
栏目:
OA
出版日期:
2010-12-08

文章信息/Info

Title:
Existence of Positive Solutions of Higher Order QuasilinearDifference Equations with Variable Delay
作者:
周效良1王五生2
(1. 广东海洋大学 数学系, 广东 湛江 524088;2. 广西河池学院 数学系, 广西 宜州 546300)
Author(s):
ZHOU Xiaoliang1WANG Wusheng2
(1. Department of Mathematics, Guangdong Ocean University, Zhanjiang 524088, Guangdong;2. Department of Mathematics, Hechi College, Yizhou 546300, Guangxi)
关键词:
正解 高阶差分方程 拟线性 时滞
Keywords:
positive solution higher order difference equation quasilinear delay2000 MSC39A10
分类号:
O175
文献标志码:
A
摘要:
对一类高阶拟线性变时滞差分方程的正解的存在性进行了研究.在构造Banach空间的基础上,对其上的算子的连续性和一致Cauchy性给予了证明,然后应用Schauder不动点定理得到了存在正解的充分条件,进而与已有结果结合得到充分必要条件.作为特例,给出了结果在著名的Emden-Fowler微分方程的离散类比方程上的应用,得到Emden-Fowler型方程的任一有界解振动的充分必要条件.为说明定理条件非空,也给出了例子进行验证.结果推广了文献中的一些结果.
Abstract:
In this paper, the existence of positive solutions of higher order quasilinear difference equations with variable delay is studied. Based on construction of Banach space and the proof of continuous and uniformly Cauchy properties, by using Schauder’s fixed point theorem, a sufficient condition which extends the known result is obtained. Two examples illustrating the validity are also given.

参考文献/References:

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备注/Memo

备注/Memo:
收稿日期:2009-04-22基金项目:国家自然科学基金(10071045)、广东省自然科学基金项目(10452408801004217)、广西省自然科学基金(0991265)和广西自治 区教委科研基金(200707MS112)资助项目作者简介:周效良(1965—),男,教授,主要从事微分方程与动力系统的研究
更新日期/Last Update: 2010-12-08