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| 一类含隅角和弯矩的奇异梁方程三个正解的存在性 | |
| 引用本文： | 赵东霞,王宏洲,王军民,赵俊芳.一类含隅角和弯矩的奇异梁方程三个正解的存在性[J].应用数学学报,2011,34(5). |
| 作者姓名： | 赵东霞 王宏洲 王军民 赵俊芳 |
| 作者单位： | 1. 中北大学理学院数学系,太原030051;北京理工大学应用数学系,北京100081 2. 北京理工大学应用数学系,北京,100081 3. 中国地质大学(北京)信息工程学院,北京,100083 |
| 基金项目： | 山西省青年基金(基金号:2009021001-2); 中央高校基本科研业务经费(预研项目)(2011YYL079); 优秀教师(2011YXL047)资助项目 |
| 摘 要： | 利用格林函数方法和Avery-Peterson不动点定理研究了一类非线性四阶两点边值问题u(4)(t) =f(t,u(t),u′(t),u″(t)), 0 ＜ t ＜ 1,u(0) =u′(1) =u″(0) =u′″(1) =0多个正解的存在性,其中允许非线性项f(t,u,v,w)在t=0,t=1,u=0,v=0,w=0处奇异.在力学上该问题模拟了左端简单支撑右端被滑动夹子夹住的弹性梁的挠曲.由于非线性项同时涉及隅角和弯矩,因此主要结论对于梁的稳定性分析是有益的.最后我们给出了一个例子,进一步证实本文理论的严密性和可行性. |
| 关 键 词： | 弹性梁方程 正解 奇性 |
Existence of Triple Positive Solutions to a Class of Singular Beam Equations with Corner and Bending Moment |
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| ZHAO DONGXIA , WANG HONGZHOU , WANG JUNMIN , ZHAO JUNFANG.Existence of Triple Positive Solutions to a Class of Singular Beam Equations with Corner and Bending Moment[J].Acta Mathematicae Applicatae Sinica,2011,34(5). | |
| Authors: | ZHAO DONGXIA WANG HONGZHOU WANG JUNMIN ZHAO JUNFANG |
| Institution: | ZHAO DONGXIA (Department of Mathematics,North university of China,Taiyuan 030051) (Department of Applied Mathematics,Beijing institute of technology,Beijing 100081) WANG HONGZHOU WANG JUNMIN (Department of Applied Mathematics,Beijing 100081) ZHAO JUNFANG (College of Information Engineering,China university of Geosciences,Beijing 100083) |
| Abstract: | By applying the technique of Green function and a fixed point theorem due to Avery and Peterson,we studied the existence of triple positive solutions for a class of nonlinear fourth-order two-point boundary value problems:u(4)(t)=f(t,u(t),u'(t)),u(0)=u'(1)=U(0)=U'(1)=0 0 |
| Keywords: | an elastic beam equation positive solutions singularity |
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