| 三阶非线性系统三点边值问题的正解(英文) |
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| 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) |
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| 作者姓名： | 何希萍 孙红蕊 |
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| 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 |
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| 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=diag[γ_1,…,γ_n],δ=diag[δ_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.
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| 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 |
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| 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) |
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| Authors: | HE Xi-Ping SUN Hong-Rui |
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| 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=diag[γ1,…,γn],δ=diag[δ1,…,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. |
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| Keywords: | nonlinear system three-point boundary value problem positive solution fixed point |
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