| 一类三阶三点边值问题正解的存在性 |
| |
| 引用本文： | 郑婷,朱思念,关琦. 一类三阶三点边值问题正解的存在性[J]. 四川理工学院学报(自然科学版), 2011, 24(3): 271-274 |
| |
| 作者姓名： | 郑婷 朱思念 关琦 |
| |
| 作者单位： | 中国矿业大学理学院,江苏徐州,221008 |
| |
| 摘 要： | 文章研究了一类三阶三点边值问题u″′(t)=a(t)f(t,u(t)),u(0)=δu(η),u″(1)=0,u′(1)=0两个正解的存在性,首先给出该边值问题的格林函数,将边值问题的解的存在性转化为一个积分算子的不动点的存在性,在适当的Banach空间中定义了一个锥,然后结合格林函数的性质,利用Krasnoselskii不动点定理研究了该边值问题正解的存在性,给出了两个正解存在的充分条件。
|
| 关 键 词： | 三阶三点 Krasnoselskii不动点定理 正解 |
Existence of Positive Solutions for a Third-order Three-point Boundary Value Problem |
| |
| ZHENG Ting,ZHU Si-nian,GUAN Qi. Existence of Positive Solutions for a Third-order Three-point Boundary Value Problem[J]. Journal of Sichuan University of Science & Engineering(Natural Science Editton), 2011, 24(3): 271-274 |
| |
| Authors: | ZHENG Ting ZHU Si-nian GUAN Qi |
| |
| Affiliation: | ZHENG Ting,ZHU Si-nian,GUAN Qi(1.College of Science,China University Mining and Technology,Xuzhou 221008,China) |
| |
| Abstract: | We study the existence of two positive solutions for the third-order three-point boundary value problem,u″′(t)=a(t)f(t,u(t)),u(0)=δu(η),u″(1)=0,u′(1)=0,the corresponding Green's function is given,we convert the existence of solutions for the boundary value problem into the existence of fixed point of an integral operator equation.A cone on a Banach space is well defined,by using Krasnoselskii's fixed point theorem combined with the properties of Green function,we establish sufficient conditions for the existence of two positive solutions to the boundary value problem. |
| |
| Keywords: | third-order three-point Krasnoselskii's fixed-point theorem positive solutions |
| 本文献已被 CNKI 万方数据 等数据库收录！ |
|
