| 三阶非线性系统三点边值问题的正解(英文) |
| |
| 引用本文： | 何希萍,孙红蕊.三阶非线性系统三点边值问题的正解(英文)[J].兰州大学学报(自然科学版),2010,46(4). |
| |
| 作者姓名： | 何希萍 孙红蕊 |
| |
| 作者单位： | 1. 甘肃广播电视大学,教学指导中心,兰州,730030;兰州大学,数学与统计学院,兰州,730000
2. 兰州大学,数学与统计学院,兰州,730000 |
| |
| 摘 要： | 研究了三阶非线性系统u′″(t)=f(t,u(t)),t∈t_1,t_3]在满足边值条件u(t_1)=u′(t_2)=0,γu(t_3)+δu″(t_3)=0下正解的存在性,其中u=(u_1,…,u_n),γ=diagγ_1,…,γ_n],δ=diagδ_1,…,δ_n].运用Leray-Schauder型非线性抉择和Krasnosel'skii不动点定理,建立了此问题单个和两个正解的存在性结果,并举例说明了所得结论的有效性.
|
| 关 键 词： | 非线性系统 三点边值问题 正解 不动点 |
Positive solutions to three-point boundary value problems for third order nonlinear systems |
| |
| HE Xi-Ping,SUN Hong-Rui.Positive solutions to three-point boundary value problems for third order nonlinear systems[J].Journal of Lanzhou University(Natural Science),2010,46(4). |
| |
| Authors: | HE Xi-Ping SUN Hong-Rui |
| |
| Abstract: | The existence of positive solutions was studied for third order nonlinear system u"'(t)=f(t,u(t)), t∈t1, t3] with the boundary conditions u(t1)=u'(t2)=0,γu(t3)+δu"(ts)=0,where u=(u1, …,un),γ=diagγ1,…,γn],δ=diagδ1,…,δn]. Some results were obtained for the existence of single and twin positive solutions for the above system by using nonlinear alternative of Leray-Schauder type and Krasnosel'skii fixed point theorem in a cone. An example was also given to illustrate the main results. |
| |
| Keywords: | nonlinear system three-point boundary value problem positive solution fixed point |
| 本文献已被 CNKI 万方数据 等数据库收录！ |
|
