| 一类含参数半正四阶边值问题的正解存在性与多解性 |
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| 引用本文： | 姚庆六. 一类含参数半正四阶边值问题的正解存在性与多解性[J]. 数学学报, 2008, 51(2): 401-410. DOI: CNKI:SUN:SXXB.0.2008-02-024 |
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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,南京210003 |
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| 摘 要： | 考察了一类含有两个参数的非线性四阶边值问题的n个解和/或正解的存在性,其中允许非线性项有一个非正的函数型下界.在力学和工程上,这类四阶边值问题描述了两端简单支撑的弹性梁的变形.主要工具是锥上的Krasnosel’skii不动点定理和局部化方法.
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| 关 键 词： | 非线性常微分方程 边值问题 正解 |
| 文章编号： | 0583-1431（2008）02-0401-10 |
| 收稿时间： | 2007-01-30 |
Positive Solutions to a Class of Semipositive Fourth-Order Boundary Value Problems with Parameters |
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| Qing Liu YAO. Positive Solutions to a Class of Semipositive Fourth-Order Boundary Value Problems with Parameters[J]. Acta Mathematica Sinica, 2008, 51(2): 401-410. DOI: CNKI:SUN:SXXB.0.2008-02-024 |
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| Authors: | Qing Liu YAO |
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| Affiliation: | Qing Liu YAO Department of Applied Mathematics, Nanjing University of Finance and Economics, Nanjing 210003, P. R. China |
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| Abstract: | The existence of n solutions and/or positive solutions is considered for a class of nonlinear fourth-order boundary value problems with two parameters, where the nonlinear term is allowed to possess a nonpositive lower bound of function type. In mechanics and engineering, the class of fourth-order boundary value problems describes the deflection of elastic beams simply supported at both ends, the Main tools used are Krasnosel'skii fixed point theorem on cone and localization method. |
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| Keywords: | nonlinear ordinary differential equation boundary value problem positive solution |
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