| 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):183~188 |
| 超线性非线性Sturm-Liouville边值问题的正解 |
| Positive Solutions of Superlinear Nonlinear Sturm-Liouville Boundary Value Problems |
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| DOI： |
| 中文关键词: 边值问题 正解 全局结构 拓扑方法 |
| 英文关键词:Boundary value problem Positive solution Global structure Topological methods |
| 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 |
| Author Name | Affiliation | E-mail | | LI Hongyu | College of Information Science and Engineering, Shandong University of Science
and Technology, Qingdao 266510, Shandong, China. | sdlhy1978@163.com; | | SUN Jingxian | Department of Mathematics, Xuzhou Normal University, Xuzhou 221116,
Jiangsu, China. | jxsun7083@sohu.com | | CUI Yujun | College of Information Science and Engineering, Shandong University of Science
and Technology, Qingdao 266510, Shandong, China. | cyj720201@163.com |
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| 中文摘要: |
| 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. |
| 英文摘要: |
| 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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