| 一类四阶非线性边值问题的解和正解 |
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| 引用本文： | 姚庆六,任立顺.一类四阶非线性边值问题的解和正解[J].厦门大学学报(自然科学版),2004,43(6):765-768. |
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| 作者姓名： | 姚庆六 任立顺 |
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| 作者单位： | 1. 南京财经大学应用数学系,江苏,南京,210046
2. 周口师范学院数学系,河南,周口,466000 |
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| 摘 要： | 利用Schauder不动点定理及积分方程组技巧研究了一类四阶非线性边值问题的解和正解的存在性.在材料力学中,这类边值问题通常描述了一端简单支撑,另一端被活动夹子夹住的弹性梁的平衡状态.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,该问题至少存在一个解或者正解.
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| 关 键 词： | 四阶边值问题 非线性弹性梁方程 解和正解 存在性 |
| 文章编号： | 0438-0479(2004)06-0765-04 |
| 修稿时间： | 2003年10月9日 |
Solution and Positive Solution to a Class of Nonlinear Fourth-order Boundary Value Problems |
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| YAO Qing-liu,REN Li-shun.Solution and Positive Solution to a Class of Nonlinear Fourth-order Boundary Value Problems[J].Journal of Xiamen University(Natural Science),2004,43(6):765-768. |
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| Authors: | YAO Qing-liu REN Li-shun |
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| Institution: | YAO Qing-liu~1,REN Li-shun~2 |
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| Abstract: | The existence of solution and positive solution is studied for a class of fourth-order nonlinear boundary value problems by using Schauder fixed point theorem and the technique of system of integral equations.In the mechanics of material,the class of problems usually describes the equilibrium state of the elastic beam in which an end is simply supported and other end is Clamped by sliding clamps.The main results show that the problem has at least one solution or positive solution provided the "maximal height" of nonlinear term on a bounded set of its domain. |
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| Keywords: | fourth-order boundary value problem nonlinear elastic beam equation solution and positive solution existence |
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