| 一类非线性项含有所有阶导数的梁方程的可解性 |
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| 引用本文： | 姚庆六. 一类非线性项含有所有阶导数的梁方程的可解性[J]. 周口师范学院学报, 2006, 23(2): 8-12 |
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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;周口师范学院,数学系,河南,周口,466000 |
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| 摘 要： | 利用Schauder不动点定理研究了一类非线性四阶边值问题的解和正解的存在性。主要工具是方程的分解技巧和二阶两点边值问题的Green函数。在力学中，这类问题描述了一端简单支撑，另一端滑动的弹性梁的形变。
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| 关 键 词： | 四阶常微分方程 边值问题 解和正解 存在性 |
| 文章编号： | 1671-9476（2006）02-0008-05 |
| 收稿时间： | 2005-12-29 |
| 修稿时间： | 2005-12-29 |
Solvability of a class of beam equations whose nonlinear term contain all-order derivatives |
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| YAO Qing-liu. Solvability of a class of beam equations whose nonlinear term contain all-order derivatives[J]. Journal of Zhoukou Normal University, 2006, 23(2): 8-12 |
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| Authors: | YAO Qing-liu |
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| Abstract: | By applying Schauder fixed point theorem, the existence solution and positive solutions is studied for a class af nonlinear fourth - order boundary value problems. Main tools are the decomposition technique and the Green functions of second - order two-point boundary value problems. In the mechanics, the class of problems describes the deformation of an elastic beam whose one end is simply supported and other is sliding. |
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| Keywords: | fourth-order ordinary differential equation boundary value problem solution and positive solution existence |
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