| 标题 | 一类奇异三阶三点边值问题的正解 |
| 范文 | 王珍 朱少平
摘 要 利用krasnoelskii锥拉伸与压缩不动点定理考察了一类奇异非线性三阶三点边值问题的正解的存在性，得到了此类边值问题在奇异条件下至少存在一个正解的结果。 关键词 三阶三点边值问题 奇异 正解 锥 不动点定理 中图分类号：O175 文献标识码：A DOI：10.16400/j.cnki.kjdks.2019.03.026 Abstract This paper is concerned with the existence of a positive solution of singular third-order three-point boundary value problem by using the Krasnoselskii's fixed point theorem of cone expansion-compression type， and established existence results for at least one positive solution for this class of problem when the nonlinear term is allowed to be singular. Keywords third-order three-point boundary value problem； singular； positive solution； cone； fixed point theorem 參考文献 [1] D.R.Anderson. Multiple positive solutions for a three-point boundary value prob- lem[J].Math Comput.Modelling，1998.27（6）：49-57. [2] Shuhong Li. Positive solutions of nonlinear singular third-order two-point bound- ary value problem[J].2005. [3] 刘希玉.具有奇性的一类边值问题的正解[J].纯粹数学和应用数学，1998.1. [4] Q. Yao.The existence and multiplicity of positive solutions for a third-order three - point boundary value problem[J].Acta Math.Appl.Sinica，2003.19：117-122. [5] D.Guo， V.Lakshmikantham.Nonlinear Problems in Abstract Cones[M].Academic Press， San Diego，1988. [6] Ma Ru-yun.Existence theorems for a second order three-point boundary value pro- blem[J].J Math Anal Appl，1997.212：430-442. [7] Ma Ru-yun. Positive solutions of a nonlinear three-point boundary value problems [J].Electron. J. Differential Equations，1999.34：1-8. [8] 郭大钧.非线性泛函分析[M].济南：山东科学技术出版社，2003. [9] 孙经先.非线性泛函分析及其应用[M].北京：科学出版社，2007. [10] 葛渭高.非线性常微分方程边值问题[M].北京：科学出版社，2007. [11] L.Guo，J.Sun，Y.Zhao. Existence of positive solutions for nonlinear third-order three-point boundary value problems[J].Nonlinear Anal.，2008.68（10）：3151 -3158. |
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