| 两端固定的非线性弹性梁方程的解和正解 |
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| 引用本文： | 姚庆六.两端固定的非线性弹性梁方程的解和正解[J].上海大学学报(自然科学版),2008,14(1):46-51. |
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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： | 考察了含有各阶导数的一个4阶非线性弹性梁方程的解和正解的存在性.在材料力学中,这个方程描述了两端固定的弹性梁的形变,而未知函数的1、2、3阶导数分别表示梁的隅角、弯矩和剪力.通过在Banach空间C 3［0，1］上选择适当的等价范数，并且利用Leray-Schauder不动点定理获得了该方程的几个存在性结论.这些结论表明,只要非线性项在其定义域的某个有界子集上的“最大高度”是适当的,该方程至少存在一个解或者正解.
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| 关 键 词： | 边值问题 非线性常微分方程 解和正解 |
| 文章编号： | 1007-2861（2008）01-0046-06 |
| 收稿时间： | 2006-09-22 |
| 修稿时间： | 2006年9月22日 |
Solution and Positive Solution to Nonlinear Equation for Elastic Beam with Both Ends Fixed |
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| YAO Qing-liu.Solution and Positive Solution to Nonlinear Equation for Elastic Beam with Both Ends Fixed[J].Journal of Shanghai University(Natural Science),2008,14(1):46-51. |
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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 of solution and positive solution is considered for a fourth order nonlinear elastic beam equation with derivatives of all orders. In material mechanics, the equation describes deformation of an elastic beam whose two ends are fixed. The first, second and third derivatives express corner, bending moment and shearing stress of the beam, respectively. By choosing suitable equivalent norm in the Banach space -C 3［0,1］ and applying the Leray-Schauder fixed point theorem, several existence results are obtained for the equation. The results show that the equation has at least one solution or positive solution provided the “maximal height” of nonlinear term is appropriate on a bounded set of its domain. |
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| Keywords: | nonlinear ordinary differential equation boundary value problem solution and positive solution |
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