具有Sturm-Liouville边界条件的四阶奇异微分方程正解的存在性

J4 ›› 2010, Vol. 45 ›› Issue (8): 76-80.

具有Sturm-Liouville边界条件的四阶奇异微分方程正解的存在性

王新华, 张兴秋

聊城大学数学科学学院, 山东聊城 252059

收稿日期:2009-12-03 出版日期:2010-08-16 发布日期:2010-09-16
作者简介:王新华(1975-),女,硕士,讲师,研究方向为非线性泛函分析.Email:wangxinhua0218163.com
基金资助:
国家自然科学基金资助项目(10871116)

Existence of positive solutions for fourth order singular differential equations with Sturm-Liouville boundary conditions

WANG Xin-hua, ZHANG Xing-qiu

College of Mathematics Sciences, Liaocheng University, Liaocheng 252059, Shandong, China

Received:2009-12-03 Online:2010-08-16 Published:2010-09-16

摘要/Abstract

摘要：

利用极值原理和上下解方法给出了具有Sturm-Liouville边界条件的四阶奇异微分方程C²［0,1］和C³［0,1］正解的存在性, 允许非线性项f(t,u)在u=0和t=0,1处可以是奇异的。

关键词: 四阶微分方程; 奇异边值问题; 上下解; 正解

Abstract:

A class of fourth order singular differential equations with Sturm-Liouville boundary conditions is investigated by the extremum principle and the upper and lower solution method. Nonlinear term f(t,u) can be singular at u=0 and t=0,1.

Key words: fourth order differential equation; singular boundary value problems; upper and lower solution; positive solutions

王新华, 张兴秋. 具有Sturm-Liouville边界条件的四阶奇异微分方程正解的存在性[J]. J4, 2010, 45(8): 76-80.

WANG Xin-hua, ZHANG Xing-qiu. Existence of positive solutions for fourth order singular differential equations with Sturm-Liouville boundary conditions[J]. J4, 2010, 45(8): 76-80.

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