东北大学学报（自然科学版）

东北大学学报(自然科学版) ›› 2008, Vol. 29 ›› Issue (11): 1669-1672.DOI: -

• 论著 • 上一篇    

一类非线性二阶三点边值问题正解的存在性

孙涛;姜秀芹;段晓东;   

  1. 东北大学理学院;大连民族学院计算机学院;
  • 收稿日期:2013-06-22 修回日期:2013-06-22 出版日期:2008-11-15 发布日期:2013-06-22
  • 通讯作者: Sun, T.
  • 作者简介:-
  • 基金资助:
    国家自然科学基金资助项目(60573124);;

Existence of positive solution to a nonlinear second-order three-point boundary value problem

Sun, Tao (1); Jiang, Xiu-Qin (1); Duan, Xiao-Dong (2)   

  1. (1) School of Sciences, Northeastern University, Shenyang 110004, China; (2) School of Computer, Dalian Nationalities University, Dalian 116600, China
  • Received:2013-06-22 Revised:2013-06-22 Online:2008-11-15 Published:2013-06-22
  • Contact: Sun, T.
  • About author:-
  • Supported by:
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摘要： 研究了一类二阶非线性常微分方程三点边值问题的正解的存在性定理,利用Krasnosel’skii不动点定理证明了当二阶非线性常微分方程三点边值问题的非线性项同是超线性时,或同是次线性时,或其中一个为超线性一个为次线性时,方程至少存在一个正解的结论.改进和推广了以往非线性项只是超线性或只是次线性时非线性三点边值问题的正解的存在性结论.所讨论的方程具有更一般的形式.

关键词: 三点边值问题, Krasnosel’skii不动点定理, 正解, 存在性

Abstract: The existence of one positive solution at least to a second-order three-point boundary value problem is studied. Several sufficient conditions for the existence of positive solution are obtained if the nonlinear terms are all superlinear or sublinear or that among them one is superlinear and the another is sublinear, based on the Krasnosel'skii fixed point theorem. The conclusion that the positive solution to a second-order three-point boundary value problem exists only if the nonlinear terms are superlinear or sublinear is thus improved and generalized.

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