数学物理学报 ›› 2017, Vol. 37 ›› Issue (2): 287-298.

• 论文 • 上一篇    下一篇

含参数四阶微分方程非局部边值问题的正解

郝新安, 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:2016-06-26 修回日期:2016-12-21 出版日期:2017-04-26 发布日期:2017-04-26
  • 通讯作者: 郝新安 E-mail:haoxinan2004@163.com
  • 基金资助:
    国家自然科学基金(11501318,11371221)、山东省自然科学基金(ZR2015AM022)和曲阜师范大学青年学术骨干培养计划国(境)外访学项目经费

Positive Solutions for Nonlocal Boundary Value Problems of Fourth Order Differential Equation with Parameters

Hao Xinan, Liu Lishan   

  1. School of Mathematical Sciences, Qufu Normal University, Shandong Qufu 273165
  • Received:2016-06-26 Revised:2016-12-21 Online:2017-04-26 Published:2017-04-26
  • Supported by:
    Supported by the NSFC (11501318, 11371221), the Natural Science Foundation of Shandong Province (ZR2015AM022) and the International Cooperation Program of Key Professors by Qufu Normal University

摘要: 通过构造特殊的锥并利用锥中的Krasnosel'skii-Zabreiko不动点定理,该文研究了含有两个参数的四阶微分方程广义Sturm-Liouville边值问题正解的存在性,推广和改进了一些已知的结果.

关键词: 正解, 积分边界条件, 不动点,

Abstract: This paper deals with the existence of positive solutions to fourth order nonlocal boundary value problems with two parameters. The proofs are based on a specially constructed cone and a fixed point theorem in a cone for a completely continuous operator, due to Krasnosel'skii and Zabreiko. The results extend and improve some known results.

Key words: Positive solution, Integral boundary conditions, Fixed point, Cone

中图分类号: 

  • O175.08