| 引用本文： |
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刘爱民,刘永建,冯春华.一类四阶奇异边值问题的正解[J].广西科学,2011,18(2):117-121. [点击复制]
- LIU Ai-min,LIU Yong-jian,FENG Chun-hua.Positive Solutions of a Singular Fourth Order Boundary Value Problem[J].Guangxi Sciences,2011,18(2):117-121. [点击复制]
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| 摘要: |
| 利用三阶两点边值问题的格林函数,结合Krasnosel'skii不动点定理,考虑梁方程u(4)(t)+g(t)F(t,u(t))=0,0 < t < 1,u(0)=u'(0)=u'(1)=u″(0)=0的边值问题,其中函数F(t,u)在边界u=0可能是奇异的,函数g(t)在边界t=0和t=1也可以是奇异的.获得该系统至少存在一个正解的几组充分条件,并用例子说明主要结果是可行的. |
| 关键词: 奇异边值问题 Krasnosel'skii不动点原理 正解 |
| DOI： |
| 投稿时间：2010-08-25修订日期：2010-12-18 |
| 基金项目:National Natural Science Foundation of China(No.10961005); the Sustentation Fund of the Elitists for Yulin Normal University(No. G2010006); the Scientific Research Foundation of Guangxi Education Office of China(No.200911LX356) |
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| Positive Solutions of a Singular Fourth Order Boundary Value Problem |
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LIU Ai-min1,2, LIU Yong-jian3, FENG Chun-hua1
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| (1.School of Mathematics Science, Guangxi Normal University, Guilin, Guangxi, 541004, China;2.Educational Technology Center, Yulin Normal University, Yulin, Guangxi, 537000, China;3.Department of Mathematics and Computation Science, Yulin Normal University, Yulin, Guangxi, 537000, China) |
| Abstract: |
| A boundary value problem for the beam equation u(4) (t)+g (t)F (t, u (t))=0, 0 < t < 1, together with boundary conditions u (0)=u' (0)=u' (1)=u″ (0)=0, is considered, where F (t, u) may be singular at u=0, g (t) may be singular at both ends t=0 and t=1.By using a Green function of third order two point boundary value problems and Krasnosel'skii fixed point theorem, some sufficient conditions for the existence of at least one positive solution for the boundary value problem are established.An example also is given to illustrate the main results. |
| Key words: singular boundary value problem Krasnosel'skii fixed point theorem positive solution |
