| 具有正Green函数的奇异Sturm-Liouville边值问题的正解 |
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| 引用本文： | 姚庆六.具有正Green函数的奇异Sturm-Liouville边值问题的正解[J].数学研究及应用,2013,33(5):561-568. |
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| 作者姓名： | 姚庆六 |
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| 作者单位： | 南京财经大学应用数学系, 江苏 南京 210003 |
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| 基金项目： | 国家自然科学基金(Grant No.11071109). |
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| 摘 要： | 考察了具有正Green函数的奇异Sturm-Liouville边值问题的正解存在性与多解性,其中相对于空间变元非线性项可以是超强奇异的.通过构造适当的控制函数,精确估计了解的先验界.利用锥压缩-拉伸型的Guo-Krasnosel'skii不动点定理,证明了几个存在结论.
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| 关 键 词： | 奇异常微分方程 Sturm-Liouville边值问题 正解 存在性与多解性. |
| 收稿时间： | 2012/5/24 0:00:00 |
| 修稿时间： | 9/3/2012 12:00:00 AM |
Positive Solutions of Singular Sturm-Liouville Boundary Value Problems with Positive Green Function |
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| Qingliu YAO.Positive Solutions of Singular Sturm-Liouville Boundary Value Problems with Positive Green Function[J].Journal of Mathematical Research with Applications,2013,33(5):561-568. |
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| Authors: | Qingliu YAO |
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| Institution: | Department of Applied Mathematics, Nanjing University of Finance and Economics, Jiangsu 210003, P. R. China |
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| Abstract: | The existence and multiplicity of positive solutions are studied for a singular Sturm-Liouville boundary value problem with positive Green function, where the nonlinearity may be super-strongly singular with respect to the space variable. By constructing suitable control functions, the a priori bound of solution is exactly estimated. By applying the Guo-Krasnosel'skii fixed point theorem of cone expansion-compression type, several existence results are proved. |
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| Keywords: | singular ordinary differential equation Sturm-Liouville boundary value problem positive solution existence and multiplicity |
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