| 一类含双参数二阶两点边值问题正解的存在性和不存在性 |
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| 引用本文： | 刘春利,杨凯丽,李军刚. 一类含双参数二阶两点边值问题正解的存在性和不存在性[J]. 甘肃科学学报, 2011, 23(2): 10-13 |
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| 作者姓名： | 刘春利 杨凯丽 李军刚 |
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| 作者单位： | 1. 西北师范大学教育学院,甘肃兰州,730070
2. 甘肃省秦安县麻湾中学,甘肃秦安,741600 |
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| 摘 要： | 运用Schauder不动点定理及上下解方法考虑二阶两点边值问题u″（t）＋λa（t）f（t,u（t））=0,a.e.t∈（0,1）,u（0）=0,u（1）=μ当参数μ,λ变化时正解的存在性和不存在性,其中λ,μ∈（0,＋∞）,f是L1-Carathéodory函数,a∈L^1（0,1）且a≥0.
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| 关 键 词： | 二阶边值问题 正解 上下解方法 Schauder不动点定理 |
Existence and Nonexistence of Positive Solutions of a Class of Second-order Two-point Boundary Value Problem with Two Parameters |
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| LIU Chun-li,YANG Kai-li,LI Jun-gang. Existence and Nonexistence of Positive Solutions of a Class of Second-order Two-point Boundary Value Problem with Two Parameters[J]. Journal of Gansu Sciences, 2011, 23(2): 10-13 |
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| Authors: | LIU Chun-li YANG Kai-li LI Jun-gang |
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| Affiliation: | 1.College of Education,Northwest Normal University,Lanzhou 730070,China; 2.Mawan Middle School,Qinan County,Qinan 741600,China) |
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| Abstract: | By using the lower and upper solutions and the Schauder fixed point theorem,we consider the existence and nonexistence of positive solutions of second-order two-point boundary value problem u″(t)+λa(t)f(t,u(t))=0,a.e.t∈(0,1),u(0)=0,u(1)=μ when parameters μ,λ are changing.Where λ,μ∈(0,+∞),f is L1-Carathéodory function,a∈L1(0,1) and a≥0. |
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| Keywords: | second-order boundary value problem positive solution lower and upper solutions Schauder fixed point theorem |
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