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变换技巧、不动点定理和一类含弯矩的梁方程的3个正解

发表时间:2015-07-15  浏览量:1520  下载量:516
全部作者: 邱镜亮
作者单位: 北京信息科技大学理学院
摘 要: 通过一种新的变换技巧处理梁方程的弯矩,并结合锥不动点定理,考察一类梁方程3个正解的存在性问题。获得了一些新的结果,并给出了正解的范数估计。因为在材料力学中四阶常微分方程描述了弹性梁的静态形变,故该研究方法和结论对于梁的稳定性分析是有益的。
关 键 词: 常微分方程;变换技巧;Leggett-Williams不动点定理;非线性弹性梁方程;3个正解
Title: Transformation technique, fixed point theory and triple positive solutions for a elastic beam equation with the bending term
Author: QIU Jingliang
Organization: School of Applied Science, Beijing Information Science & Technology University
Abstract: Using a new technique for dealing with the bending term of beam equations, we consider the existence of triple positive solutions for a beam equation. Besides achieving new results, estimates on the norms of these solutions are also provided. Since fourth ordinary differential equations describe the stationary states of the deflection of an elastic beam in the material mechanics, the results and method are useful for the stability analysis of the beam.
Key words: ordinary differential equation; transformation technique; Leggett-Williams’s fixed point theorem; nonlinear elastic beam equation; three positive solutions
发表期数: 2015年7月第13期
引用格式: 邱镜亮. 变换技巧、不动点定理和一类含弯矩的梁方程的3个正解[J]. 中国科技论文在线精品论文,2015,8(13):1367-1373.
 
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