四阶非线性边值问题解的存在性与上下解方法

数学物理学报 ›› 2003, Vol. 23 ›› Issue (2): 245-252.

四阶非线性边值问题解的存在性与上下解方法

李永祥

西北师范大学数学系兰州 730070

出版日期:2003-04-25 发布日期:2003-04-25
基金资助:
甘肃省自然科学基金(ZS991A25007Z)、数学天元基金和西北师范大学科技创新工程基金(NWNUKJCXGC212)资助项目

Existence and Method of Lower and Upper Solutions for Fourth Order Nonlinear Boundary Value Problems

LI Yong-Xiang

西北师范大学数学系兰州 730070

Online:2003-04-25 Published:2003-04-25
Supported by:
甘肃省自然科学基金(ZS991A25007Z)、数学天元基金和西北师范大学科技创新工程基金(NWNUKJCXGC212)资助项目

摘要/Abstract

摘要：

该文讨论四阶常微分方程边值问题u^(4)(t)=f(t,u,u″), t∈［0,1］,u(0)=u(1)=u″(0)=u″(1)=0解的存在性, 其中f(t,u,v):［0,1］×R×R→R为Carathéodory函数. 在不限制f关于u,v的增长阶, 不假定f关于u,v的单调性的一般情形下, 用上下解方法获得了解的存在性结果,并讨论了单调迭代求解的有效性.

关键词: 四阶边值问题;弱极值原理;二阶积微分方程;上解;下解

Abstract:

This paper studies the existence of solutions for the fou rthorder boundary value problem u^(4)(t) = f(t,u(t),u″(t)), t∈［0,1］,u(0)=u(1)=u″(0)=u″(1)=0,where f: ［0,1］×R×R→R is a Carathéodory function. In the general case without restriction for growth condition of f and assumption of monotonicity on f, the author obtains the existence results of solution by using the met hod of lower and upper solutions. The validity of finding solutions with the mo notone iterative method is also discussed.
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Key words: Fourth order boundary value problem, Weak maximum princ iple, Second order integro differential equation, Lower and upper solution.

中图分类号:

34B15

李永祥. 四阶非线性边值问题解的存在性与上下解方法[J]. 数学物理学报, 2003, 23(2): 245-252.

LI Yong-Xiang. Existence and Method of Lower and Upper Solutions for Fourth Order Nonlinear Boundary Value Problems[J]. Acta mathematica scientia,Series A, 2003, 23(2): 245-252.

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