| 两参数非线性四阶边值问题的可解性 |
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| 引用本文： | 姚庆六.两参数非线性四阶边值问题的可解性[J].安徽大学学报(自然科学版),2008,32(5). |
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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： | 利用全连续映像的Leray-Schauder不动点定理,对含有各阶导数的两参数非线性四阶边值问题建立了一个解的存在定理.这个定理表明如果非线性项是在某个有界集合上的"高度"的积分是适当的,该问题至少有一个解.在力学上,这个问题描述了两个端点被简单支撑的弹性梁的形变.
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| 关 键 词： | 四阶常微分方程 两点边值问题 非线性 存在性 |
Solvability of nonlinear fourth-order boundary value problems with two parameters |
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| YAO Qing-liu.Solvability of nonlinear fourth-order boundary value problems with two parameters[J].Journal of Anhui University(Natural Sciences),2008,32(5). |
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| Authors: | YAO Qing-liu |
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| Abstract: | An existence theorem of solution was established for a nonlinear fourth-order boundary value problem with two parameters and all order derivatives by using the Leray-Schauder fixed point theorem concerned with completely continuous mapping.The theorem showed that the problem had at least a solution if the integration of "height" of nonlinear term on some bounded set was appropriate.In mechanics,the problems described the deformations of an elastic beam simply supported at both ends. |
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| Keywords: | fourth-order ordinary differential equation two-point boundary value problem nonlinearity existence |
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