| 超线性非线性Sturm-Liouville边值问题的正解 |
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| 引用本文： | 李红玉,孙经先,崔玉军.超线性非线性Sturm-Liouville边值问题的正解[J].数学年刊A辑,2010,31(2). |
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| 作者姓名： | 李红玉 孙经先 崔玉军 |
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| 作者单位： | 1. 山东科技大学信息科学与工程学院,山东青岛,266510
2. 徐州师范大学数学系,江苏徐州,221116 |
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| 基金项目： | 国家自然科学基金，山东科技大学科学研究春营计划 |
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| 摘 要： | 利用拓扑方法讨论了一类非线性Sturm-Liouville边值问题{-u″=λf(x,u),0≤x≤1,α0u(0)+β0u′(0)=0, α1u(1)+β1u′(1)=0.研究了上述问题的正解的全局结构,在非线性项f(x,u)不满足条件f(x,u)≥0(u≥0)时获得了正解的存在性.
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| 关 键 词： | 边值问题 正解 全局结构 拓扑方法 |
Positive Solutions of Superlinear Nonlinear Sturm-Liouville Boundary Value Problems |
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| LI Hongyu,SUN Jingxian,CUI Yujun.Positive Solutions of Superlinear Nonlinear Sturm-Liouville Boundary Value Problems[J].Chinese Annals of Mathematics,Series A,2010,31(2). |
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| Authors: | LI Hongyu SUN Jingxian CUI Yujun |
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| Abstract: | The following nonlinear Sturm-Liouville problem {-u″=λf(x,u),0≤x≤1,α0u(0)+β0u′(0)=0, α1u(1)+β1u′(1)=0.is discussed by topological methods. The global structure of the set of positive solutions to the above problem is obtained, and the existence of positive solutions of the above problem is proven under the condition that the nonlinear term f(x, u) does not satisfy f(x, u) ≥0 (u ≥0). |
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| Keywords: | Boundary value problem Positive solution Global structure Topological methods |
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