| 两端固定的弱半正梁方程的解和正解 |
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| 引用本文： | 姚庆六. 两端固定的弱半正梁方程的解和正解[J]. 山东大学学报(理学版), 2006, 41(6): 6-10 |
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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,江苏,南京,210003 |
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| 摘 要： | 考察了两个端点固定的非线性四阶弹性梁方程的解和正解的存在性与多解性, 其中非线性项可以没有下界.主要工具是积分方程技巧 和锥上的不动点定理.所有存在性与多解性结论都依赖于非线 性项在某些有界集上的“高度”,同时与非线性项在这些有界集合以 外的增长无关.
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| 关 键 词： | 非线性常微分方程 边值问题 解 正解 存在性 多解性 |
| 文章编号： | 1671-9352（2006）06-0006-05 |
| 收稿时间： | 2006-05-10 |
| 修稿时间： | 2006-05-10 |
Solutions and positive solutions of a weaksemipositone beam equation fixed at both ends |
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| YAO Qing-liu. Solutions and positive solutions of a weaksemipositone beam equation fixed at both ends[J]. Journal of Shandong University, 2006, 41(6): 6-10 |
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| Authors: | YAO Qing-liu |
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| Affiliation: | Department of Applied Mathematics, Nanjing University of Finance and Economics, Nanjing 210003, Jiangsu, China |
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| Abstract: | The existence and multiplicity of solutionsand positive solutions for a nonlinear elastic beam equations fixed at both ends are considered,where nonlinear term may not have lower bound.Main ingredients are the technology of integral equation and the fixed point theorems on cone.All conclusions about existence and multiplicity depend upon the "heights" of nonlinear term on some bounded sets,while they are independent of the growths of nonlinear term outside these sets. |
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| Keywords: | nonlinear ordinary differential equation boundary value problem solution positive solution existence multiplicity |
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