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

• 论文 • 上一篇    下一篇

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   

  1. 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   

  1. College of Mathematics Sciences, Liaocheng University, Liaocheng 252059, Shandong, China
  • Received:2009-12-03 Online:2010-08-16 Published:2010-09-16

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

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