| 一类含隅角和弯矩的梁方程的正解存在性与多解性 |
| |
| 引用本文： | 姚庆六.一类含隅角和弯矩的梁方程的正解存在性与多解性[J].兰州大学学报(自然科学版),2006,42(4):127-130. |
| |
| 作者姓名： | 姚庆六 |
| |
| 作者单位： | 南京财经大学,应用数学系,江苏,南京,210003 |
| |
| 摘 要： | 利用锥上的Krasnosel'skii不动点定理考察了非线性项含有隅角和弯矩的四阶弹性梁方程{u(4)(t)=f(t,u(t),u'(t),u"(t)),0≤t≤1,u(0)=u(1)=u"(0)=u"(1)=0的正解.在材料力学中,该方程描述了一类两端简单支撑的弹性梁的形变.结论表明这个方程可以具有n个正解,只要非线性项在某些有界集上的"高度"是适当的,其中n是一个任意的自然数.
|
| 关 键 词： | 非线性弹性梁方程 边值问题 正解 存在性 多解性 |
| 文章编号： | 0455-2059（2006）04-0127-04 |
| 收稿时间： | 2004-04-02 |
| 修稿时间： | 2004-04-022006-04-20 |
Existence and multiplicity of positive solutions to a class of beam equations with corner and bending moment |
| |
| YAO Qing-liu.Existence and multiplicity of positive solutions to a class of beam equations with corner and bending moment[J].Journal of Lanzhou University(Natural Science),2006,42(4):127-130. |
| |
| Authors: | YAO Qing-liu |
| |
| Institution: | Department of Applied Mathematics, Nanjing University of Finance and Economics, Nanjing 210003, China |
| |
| Abstract: | By using the Krasnosel'skii fixed point theorem on cone, the positive solutions are considered for the fourth-order elastic beam equation with corner and bending moment In the material mechanics, the equation describes the deformation of an elastic beam whose both ends are simply supported. Our results show that the equation may have n positive solutions provided the "heights" of nonlinear term are appropriate on some bounded sets, where n is an arbitrary natural number. |
| |
| Keywords: | nonlinear elastic beam equation boundary value problem positive solution existence multiplicity |
| 本文献已被 CNKI 维普 万方数据 等数据库收录！ |
|
