| 奇异微分方程的广义Sturm--Liouville边值问题正解的存在性 |
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| 引用本文： | 杨景保,韦忠礼. 奇异微分方程的广义Sturm--Liouville边值问题正解的存在性[J]. 数学研究及应用, 2011, 31(5): 801-813. DOI: 10.3770/j.issn:1000-341X.2011.05.005 |
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| 作者姓名： | 杨景保 韦忠礼 |
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| 作者单位： | 亳州师范高等专科学校理科系, 安徽 蒙城 233500;山东建筑大学理学院, 山东 济南 250101; 山东大学数学学院, 山东 济南 250100 |
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| 基金项目： | 国家自然科学基金(Grant No.10971046),安徽省自然科学基金 (Grant No.KJ2009B093),山东省自然科学基金(Grant No.ZR2009AM004),毫州高等专科学校研究项目(Grant No.BSKY0805). |
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| 摘 要： | By employing the fixed point theorem of cone expansion and compression of norm type, we investigate the existence of positive solutions of generalized Sturm-Liouville boundary value problems for a nonlinear singular differential equation with a parameter. Some sufficient conditions for the existence of positive solutions are established. In the last section, an example is presented to illustrate the applications of our main results.
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| 关 键 词： | generalized Sturm-Liouville boundary value problems second-order differential equations positive solutions. |
| 收稿时间： | 2009-11-22 |
| 修稿时间： | 2010-05-28 |
Existence of Positive Solutions of Generalized Sturm-Liouville Boundary Value Problems for a Singular Differential Equation |
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| Jing Bao YANG and Zhong Li WEI. Existence of Positive Solutions of Generalized Sturm-Liouville Boundary Value Problems for a Singular Differential Equation[J]. Journal of Mathematical Research with Applications, 2011, 31(5): 801-813. DOI: 10.3770/j.issn:1000-341X.2011.05.005 |
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| Authors: | Jing Bao YANG and Zhong Li WEI |
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| Affiliation: | 1. Department of Sciences, Bozhou Teachers College, Anhui 233500, P. R. China
2. School of Sciences, Shandong Jianzhu University, Shandong 250101, P. R. China;School of Matheraatics, Shandong University, Shandong 250100, P. R. China |
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| Abstract: | By employing the fixed point theorem of cone expansion and compression of norm type, we investigate the existence of positive solutions of generalized Sturm-Liouville boundary value problems for a nonlinear singular differential equation with a parameter. Some sufficient conditions for the existence of positive solutions are established. In the last section, an example is presented to illustrate the applications of our main results. |
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| Keywords: | generalized Sturm-Liouville boundary value problems second-order differential equations positive solutions. |
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