| 四阶非线性边值问题解的存在性与上下解方法 |
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| 引用本文： | 李永祥. 四阶非线性边值问题解的存在性与上下解方法[J]. 数学物理学报(A辑), 2003, 23(2): 245-252 |
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| 作者姓名： | 李永祥 |
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| 作者单位： | 西北师范大学数学系 兰州730070 |
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| 基金项目： | 甘肃省自然科学基金( ZS991 -A2 5 -0 0 7-Z)，数学天元基金，西北师范大学科技创新工程基金 ( NWNU-KJCXGC-2 1 2 )资助项目 |
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| 摘 要： | 该文讨论四阶常微分方程边值问题u^(4)(t)=f(t,u,u″), t∈［0,1］,u(0)=u(1)=u″(0)=u″(1)=0解的存在性, 其中f(t,u,v):［0,1］×R×R→R为Carathéodory函数. 在不限制f关于u,v的增长阶, 不假定f关于u,v的单调性的一般情形下, 用上下解方法获得了解的存在性结果,并讨论了单调迭代求解的有效性.
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| 关 键 词： | 四阶边值问题 弱极值原理 二阶积微分方程 上解 下解 |
| 文章编号： | 1003-3998(2003)02-245-08 |
Existence and Method of Lower and Upper Solutions for Fourth-Order Nonlinear Boundary Value Problems |
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| LI Yong-Xiang. Existence and Method of Lower and Upper Solutions for Fourth-Order Nonlinear Boundary Value Problems[J]. Acta Mathematica Scientia, 2003, 23(2): 245-252 |
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| Authors: | LI Yong-Xiang |
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| Abstract: | This paper studies the existence of solutions for the fou rth order boundary value problem u^(4)(t) = f(t,u(t),u″(t)), t∈［0,1］,u(0)=u(1)=u″(0)=u″(1)=0,where f: ［0,1］×R×R→R is a Carathéodory function. In the general case without restriction for growth condition of f and assumption of monotonicity on f, the author obtains the existence results of solution by using the met hod of lower and upper solutions. The validity of finding solutions with the mo notone iterative method is also discussed. |
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| Keywords: | Fourth order boundary value problem Weak maximum principle Second order integro differential equation Lower and upper solution. |
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