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| 一类奇异次线性Sturm Liouville 边值问题 | |
| 引用本文： | 姚庆六. 一类奇异次线性Sturm Liouville 边值问题[J]. 山东大学学报(理学版), 2009, 44(10): 36-38 |
| 作者姓名： | 姚庆六 |
| 作者单位： | 南京财经大学应用数学系, 江苏 南京 210003 |
| 基金项目： | 国家自然科学基金资助项目(10871059) |
| 摘 要： | 研究了一类次线性Sturm-Liouville边值问题的正解, 其中允许非线性项f(t,u)在t=0, t=1和u=0处奇异.主要工具是相关线性问题的Green函数及相应的Hammerstein积分方程。通过考察非线性项在u=0和u=+∞处的增长特性并且利用锥上的Guo-Krasnosel'skii不动点定理证明了一个新的存在定理。 |
| 关 键 词： | 奇异常微分方程 Sturm-Liouville 边值问题 正解 存在定理 |
| 收稿时间： | 2009-03-10 |
A class of singular sublinear Sturm-Liouville boundary value problems |
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| Affiliation: | Department of Applied Mathematics, Nanjing University of Finance and Economics, Nanjing 210003, Jiangsu, China |
| Abstract: | The positive solution is studied for a class of sublinear Sturm-Liouville boundary value problems, where the nonlinear term f(t,u) is allowed to be singular at t=0, t=1and u=0.The main tools are the Green function of the related linear problem and the corresponding Hammerstein integral equation. By nsidering the growth features of the nonlinear term at u=0 and u=+∞,and applying the Guo-Krasnosel'skii fixed point theorem on a cone, a new existence theorem is proved |
| Keywords: | singular ordinary differential equation Sturm-Liouville boundary value problem positive solution existence theorem |
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