| 奇异二阶微分方程积分边值问题正解的存在唯一性 |
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| 引用本文： | 张兴秋. 奇异二阶微分方程积分边值问题正解的存在唯一性[J]. 系统科学与数学, 2010, 10(10): 1407-1416 |
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| 作者姓名： | 张兴秋 |
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| 作者单位： | 华中科技大学数学与统计学院,武汉430074;聊城大学数学科学学院,聊城252059 |
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| 基金项目： | 山东省高等学校科技计划项目，国家自然科学基金，聊城大学科研启动基金 |
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| 摘 要： | 利用上下解方法结合极值原理研究一类带积分边值条件的奇异二阶微分方程正解的存在性以及唯一性,给出了$C[0,1]$和$C^1[0,1]$正解存在唯一的一个充分条件.非线性项允许在$t=0,1$ 和$x=0$处具有奇异性.
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| 关 键 词： | 奇异方程 积分边值问题 上下解 正解. |
| 收稿时间： | 2008-08-28 |
EXISTENCE AND UNIQUENESS OF POSITIVE SOLUTION FOR SECOND ORDER SINGULAR DIFFERENTIAL EQUATION WITH INTEGRAL BOUNDARY CONDITIONS |
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| ZHANG Xingqiu. EXISTENCE AND UNIQUENESS OF POSITIVE SOLUTION FOR SECOND ORDER SINGULAR DIFFERENTIAL EQUATION WITH INTEGRAL BOUNDARY CONDITIONS[J]. Journal of Systems Science and Mathematical Sciences, 2010, 10(10): 1407-1416 |
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| Authors: | ZHANG Xingqiu |
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| Affiliation: | School of Mathematics and Statistics, Huazhong University of Science and Technology, 430074; School of Mathematics, Liaocheng University, 252059 |
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| Abstract: | By applying upper and lower solutions method together with maximal principle, the existence and uniqueness of positive solutions for a class of second order singular differential equations with integral boundary value problems are investigated. Sufficient conditions for the existences and uniqueness of $C[0,1]$ positive solution as well as $C^1[0,1]$ are given. The nonlinearity $f(t,x)$ may be singular at $t=0,1$ and $x=0$. |
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| Keywords: | Singular equation integral boundary-value problem lower and upper solution positive solution. |
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