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| 一类二阶常微分方程边值问题的三个解 | |
| 引用本文： | 舒小保,朱全新. 一类二阶常微分方程边值问题的三个解[J]. 中山大学学报(自然科学版), 2005, 44(6): 5-7 |
| 作者姓名： | 舒小保 朱全新 |
| 作者单位： | 1. 中山大学数学系,广东,广州,510275 2. 华南师范大学数学系,广东,广州,510631 |
| 基金项目： | 中国科学院资助项目，高等学校博士学科点专项科研项目，广东省博士启动基金 |
| 摘 要： | 利用变分原理和Morse理论--不同于通常的不动点理论--研究了一类带参数非自治的二阶常微分方程边值问题的多重解.得出了此类方程存在3个解的充分条件. |
| 关 键 词： | 变分原理 Morse理论 边值问题 临界点 3个解 |
| 文章编号： | 0529-6579(2005)06-0005-03 |
| 收稿时间： | 2004-11-24 |
| 修稿时间： | 2004-11-24 |
Three Solutions for a Class of Boundary Value Problems of Second-Order Ordinary Differential Equations |
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| SHU Xiao-bao,ZHU Quan-xin. Three Solutions for a Class of Boundary Value Problems of Second-Order Ordinary Differential Equations[J]. Acta Scientiarum Naturalium Universitatis Sunyatseni, 2005, 44(6): 5-7 | |
| Authors: | SHU Xiao-bao ZHU Quan-xin |
| Affiliation: | 1. Department of Mathematics, Sun Yat-sen University, Guangzhou 510275, China; 2. Department of Mathematics, South China Normal University, Guangzhou 510631, China |
| Abstract: | By means of variational structure and Morse theory, which differs from common methods of fixed point theory, triple solutions of boundary value problems for a class of second-order nonautonomous ordinary differential equations with a parameter are obtained. |
| Keywords: | variational structure Morse theory boundary value problem critical point three solutions |
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