| 非线性微分方程三阶三点边值问题两个正解的存在性 |
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| 引用本文： | 郭丽君.非线性微分方程三阶三点边值问题两个正解的存在性[J].北华大学学报(自然科学版),2016(5):566-571. |
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| 作者姓名： | 郭丽君 |
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| 作者单位： | 兰州交通大学博文学院,甘肃 兰州,730101 |
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| 基金项目： | 甘肃省高等学校科研项目教育厅立项(2015B-214) |
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| 摘 要： | 考虑以下三阶三点边值问题:u'(t)+a(t)f(u(t))=0,t∈(0,1);u(0)=u″(0)=0,u'(1)-αu(η)=λ,其中0η1,0α1/η,λ∈(0,∞),通过建立相关线性边值问题的格林函数得到解的形式,运用不动点指数理论建立了上述边值问题至少两个正解的存在性准则.
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| 关 键 词： | 三阶三点边值问题 正解 存在性 锥 格林函数 不动点指数理论 |
Existence of Two Positive Solutions for Third-Order Three-Point Boundary Value Problems of Nonlinear Differential Equations |
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| Abstract: | We concerned with the following third-order three-point boundary value problem u?(t)+a(t)f(u(t))=0, t∈(0,1),u(0)=u″(0)=0, u′(1)-αu(η)=λ,{where 0<η<1,0<α<1/η,λ∈(0,￥) is a parameter. By establishing Green function for the associated linear boundary value problem, the solution for the above boundary value problem is obtained. Then the existence criterion of at least two positive solutions for the above boundary value problem is obtained by using fixed point index theorem. |
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| Keywords: | third-order three-point boundary value problem positive solution existence cone Green function fixed point index theorem |
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