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| Lidstone边值问题多个单调正解的存在性 | |
| 引用本文： | 江卫华,王 斌,刘秀君. Lidstone边值问题多个单调正解的存在性[J]. 河北科技大学学报, 2007, 28(2): 90-96,102 |
| 作者姓名： | 江卫华 王 斌 刘秀君 |
| 作者单位： | 河北科技大学理学院,河北石家庄,050018;河北化工医药职业技术学院基础部,河北石家庄,050031 |
| 基金项目： | 国家自然科学基金 , 河北省自然科学基金 , 河北省博士科研项目 , 河北省科技攻关项目 |
| 摘 要： | 对含有各阶导数的2m阶微分方程:y(2m)(t)=f(t,y(t),y′(t),…,y(2m-2)(t),y(2m-1)(t)),t∈(0,1),y(2i+1)(0)=y(2i)(1)=0,0≤i≤m-1,其中(-1)mf:[0,1]×R2m→[0,∞)是连续的。笔者首先给出方程的Green函数及其一些性质,并赋予f一定的增长条件,利用5个泛函的不动点定理,然后给出上述边值问题的3个单调正解的存在性。 |
| 关 键 词： | 高阶m点边值问题 锥 正解 Green’s函数 5个泛函的不动点定理 |
| 文章编号： | 1008-1542（2007）02-0090-07 |
| 收稿时间： | 2006-11-09 |
| 修稿时间： | 2006-11-092007-01-18 |
Existence of multiple monotone positive solutions for Lidstone boundary value problem |
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| JIANG Wei-hu,WANG Bin and LIU Xiu-jun. Existence of multiple monotone positive solutions for Lidstone boundary value problem[J]. Journal of Hebei University of Science and Technology, 2007, 28(2): 90-96,102 | |
| Authors: | JIANG Wei-hu WANG Bin LIU Xiu-jun |
| Affiliation: | 1. College of Sciences, Hebei University of Science and Technology, Shijiazhuang Hebei 050018, China; 2. Department of Basic Courses, Hebei Professional and Technological College of Chemical and Pharmaceutical Engineering, Shijiazhuang Hebei 050031, China |
| Abstract: | We discuss the following BVPy(2m)(t)=f(t,y(t),y′(t),…,y(2m-2)(t),y(2m-1)(t)),t∈(0,1),y(2i+1)(0)=y(2i)(1)=0,0≤i≤m-1,where(-1)mf:×R2m→[0,∞) is continuous.The associated Green's function for the above problem and some of its properties are given.Growth conditions are imposed on f which ensure the existence of positives.By using the 5 functionals fixed point theorem,the existence of at least 3 positive solutions for the the boundary value problem is given. |
| Keywords: | high order m-point boundary value problem cone positive solution Green's function five functionals fixed point theorem |
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