[1]李嫣红,李永祥*.一类完全三阶边值问题的上下解方法[J].四川师范大学学报(自然科学版),2018,(03):343-347.[doi:10.3969/j.issn.1001-8395.2018.03.011]
 LI Yanhong,LI Yongxiang.The Upper and Lower Solution Method for a Class of Fully Third-Order Boundary Value Problems[J].Journal of SichuanNormal University,2018,(03):343-347.[doi:10.3969/j.issn.1001-8395.2018.03.011]
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一类完全三阶边值问题的上下解方法()
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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:
2018年03期
页码:
343-347
栏目:
基础理论
出版日期:
2018-03-15

文章信息/Info

Title:
The Upper and Lower Solution Method for a Class of Fully Third-Order Boundary Value Problems
文章编号:
1001-8395(2018)03-0343-05
作者:
李嫣红 李永祥*
西北师范大学 数学与统计学院, 甘肃 兰州 730070
Author(s):
LI Yanhong LI Yongxiang
College of Mathematics and Statistics, Northwest Normal University, Lanzhou 730070, Gansu
关键词:
完全三阶边值问题 上下解 Nagumo条件 Leray-Schauder不动点定理
Keywords:
fully third-order boundary value problem lower and upper solution Nagumo condition Leray-Schauder fixed-point index
分类号:
O175.15; O177.91
DOI:
10.3969/j.issn.1001-8395.2018.03.011
文献标志码:
A
摘要:
讨论完全三阶边值问题{-u(t)=f(t,u(t),u'(t),u″(t)), t∈[0,1], u(0)=u'(0)=u″(1)=0解的存在性与唯一性,其中f:[0,1]×R3→R连续.在非线性项f(t,x,y,z)关于z满足适当的Nagumo条件下,运用特殊的截断技巧、Leray-Schauder不动点定理及上下解方法,获得了该方程解的存在性与唯一性结果.
Abstract:
In this paper, we discuss the existence and uniqueness of solution for the fully third-order boundary value problems {-u(t)=f(t,u(t),u'(t),u″(t)), t∈[0,1], u(0)=u'(0)=u″(1)=0 where f:[0,1]×R3→R is continuous. When f satisfies the proper Nagumo condition on z, we obtain the existence and uniqueness of solution for this equation via a special truncating technique, the Leray-Schauder fixed point theorem, and the lower and upper solution method.

参考文献/References:

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备注/Memo

备注/Memo:
收稿日期:2017-05-24 接受日期:2017-09-01
基金项目:国家自然科学基金(11261053和11661071)
*通信作者简介:李永祥(1963—),男,教授,主要从事非线性泛函分析的研究,E-mail:Liyx@nwnu.edu.cn
更新日期/Last Update: 2018-03-15