| 一类半正奇异Sturm-Liouville边值问题的正解 |
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| 引用本文： | 李志龙.一类半正奇异Sturm-Liouville边值问题的正解[J].数学进展,2010(1). |
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| 作者姓名： | 李志龙 |
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| 作者单位： | 江西财经大学信息管理学院; |
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| 基金项目： | 国家自然科学基金项目(No.10626029,No.10701040); 江西省教育厅科技项目(No.GJJ08358,No.GJJ08359); 江西省教改项目(No.JXJG07436); 江西财经大学青年项目(No.04232015,No.JXCDJG0813). |
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| 摘 要： | 本文讨论了一类半正奇异Sturm-Liouville边值问题正解的存在性,其中非线性项f(t,u)关于t=0,1和u=0奇异.在非线性项可取负值且下方无界的情形下,利用不动点指数理论以及线性算子的特征值理论得到了该问题正解存在性结果.
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| 关 键 词： | Sturm-Liouville边值问题 正解 不动点指数 第一特征值 |
Solutions for a Class of Singular Semipositone Sturm-Liouville Boundary Value Problem |
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| LI Zhilong.Solutions for a Class of Singular Semipositone Sturm-Liouville Boundary Value Problem[J].Advances in Mathematics,2010(1). |
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| Authors: | LI Zhilong |
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| Institution: | LI Zhilong (School of Informational Management,Jiangxi University of Finance , Economic,Nanchang,Jiangxi,330013,P.R.China) |
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| Abstract: | In this paper,we studied the existence of positive solutions for a class of semipositone singular Sturm-Liouville boundary value problem,f(t,u) is singular at t=0,1 and u=0.With the assumption that/is neither nonnegative nor below bounded,we obtained the existence of the positive solutions by using the theory about fixed point index and the theory about the eigenvalue of linear operators. |
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| Keywords: | Sturm-Liouville boundary value problem positive solutions fixed point index the first eigenvalue |
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