数学物理学报 ›› 2012, Vol. 32 ›› Issue (5): 996-1010.

• 论文 • 上一篇    

一类半正非线性多点边值问题多个正解的存在性

张新光1|潘传中2*   

  1. 1.烟台大学数学院 山东烟台 264005|2.达州职业技术学院 四川达州 510006
  • 收稿日期:2011-09-19 修回日期:2012-05-22 出版日期:2012-10-25 发布日期:2012-10-25
  • 基金资助:

    国家自然科学基金(11071141)和山东省自然科学基金(ZR2010AM017)资助

Exsitence of Multiple Positive Solutions for a Semipositone Nonlinear Multi-point Boundary Value Problems

 ZHANG Xin-Guang1, PAN Chuan-Zhong2*   

  1. 1.Department of Mathematics and Informational Sciences, Yantai University, Shandong |Yantai 264005; 2.Dazhou Vocational and Technical College, Sichuan |Dazhou |510006
  • Received:2011-09-19 Revised:2012-05-22 Online:2012-10-25 Published:2012-10-25
  • Supported by:

    国家自然科学基金(11071141)和山东省自然科学基金(ZR2010AM017)资助

摘要:

在适当的局部条件和超线性或次线性条件下, 建立了一类具有半正非线性项的多点边值问题多个正解的存在性. 扩充和提高了相关文献中两点和多点边值问题的许多结果, 尤其是半正和正定的情况.

关键词: 奇异边值问题, 半正问题, 正解, 不动点,

Abstract:

Under some suitable local conditions and superlinear or sublinear conditions, we establish the multiplicity of positive solutions for a class of singular semipositone multi-point boundary value problem. Our results extend and improve some existing results of previous literatures for two-point and multi-point boundary value problems in the positone and in the semipositone cases.

Key words: Singular boundary value problems, Semipositone,  Positive solutions, Fixed point, Cone

中图分类号: 

  • 34B15