数学物理学报 ›› 2012, Vol. 32 ›› Issue (1): 246-256.

• 论文 • 上一篇    

Banach 空间中分数阶微分方程$m$点边值问题的正解

王永庆, 刘立山   

  1. 曲阜师范大学数学科学学院 山东 曲阜 273165
  • 收稿日期:2010-07-29 修回日期:2011-05-30 出版日期:2012-02-25 发布日期:2012-02-25
  • 基金资助:

    国家自然科学基金(11071141, 10771117, 11101237)、山东省自然科学基金(ZR2011AQ008)和曲阜师范大学博士科研启动经费(Bsqd2007040)资助

Positive Solutions for Fractional m-Point Boundary Value Problem in Banach Spaces

 WANG Yong-Qing, LIU Li-Shan   

  1. School of Mathematical Sciences, Qufu Normal University, Shandong Qufu 273165)
  • Received:2010-07-29 Revised:2011-05-30 Online:2012-02-25 Published:2012-02-25
  • Supported by:

    国家自然科学基金(11071141, 10771117, 11101237)、山东省自然科学基金(ZR2011AQ008)和曲阜师范大学博士科研启动经费(Bsqd2007040)资助

摘要:

该文在Banach空间中研究一类分数阶微分方程$m$点边值问题, 证明了格林函数的性质, 构造一个特殊的锥,利用锥拉伸压缩不动点定理得到了该边值问题正解的存在性,最后给出一个例子用以说明主要结果.

关键词: 分数阶微分方程, m点边值问题, 正解,

Abstract:

In this paper, we concider a class of fractional m-point boundary value problem in Banachspaces. First, we get properties ofthe Green function, then construct a special cone and establish the existence results of positive solutions by using the cone expasion and compression fixed point theorem. Finally, an example is given to illustrate the main results of this paper.

Key words: Fractional differential equation, m-point boundary value problem, Positive solu-tion, Cone

中图分类号: 

  • 34G20