中山大学学报自然科学版 ›› 2012, Vol. 51 ›› Issue (1): 25-29.

• 研究论文 • 上一篇    下一篇

一类四阶边值问题的正解的存在性与多重性

王云杰1,朱 江2   

  1. (1徐州师范大学科文学院, 江苏 徐州 221116;2徐州师范大学数学科学学院,江苏 徐州 221116)
  • 收稿日期:2011-04-12 修回日期:1900-01-01 出版日期:2012-01-25 发布日期:2012-01-25

The Existence and Multiplicity of Positive Solutions for a Class of Fourth Order Boundary Value Problem

WANG Yunjie1,ZHU Jiang2   

  1. ( 1. Kewen Institute of Xuzhou Normal University, Xuzhou 221116, China;2. School of Mathematical Science, Xuzhou Normal University, Xuzhou 221116, China)
  • Received:2011-04-12 Revised:1900-01-01 Online:2012-01-25 Published:2012-01-25

摘要:

为了进一步发展和完善四阶边值问题正解的存在性理论,研究了下面的四阶边值问题
{u(4) =f(t,u(t),u′(t),u″(t),u(t)),0≤t≤1

u′(0)=u″(0)=u(0)=0,

ku(1)=u(1)其中,f:[0,1]×R4→[0,+∞)连续。利用锥上不动点定理得到了该四阶边值问题正解的存在性及多重性。推广了某些已知的结果。

关键词: 四阶边值问题, 正解的存在性, 不动点定理,

Abstract:

In order to develop and improve the theory about existence of positive solutions of fourth order boundary value problem,the following fourth order boundary value problem {u(4) =f(t,u(t),u′(t),u″(t),u(t)),0≤t≤1

u′(0)=u″(0)=u(0)=0,

ku(1)=u(1)

is considered, where f:[0,1]×R4→[0,+∞) is continuous. By use of the fixed point theorem in cone, the existence and multiplicity of positive solutions are obtained to the above boundary value problem. The results generalize some recent ones.

Key words: fourth order boundary value problem, the existence of positive solutions, fixed point theorem, cone

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