| 离散广义Emden-Fowler方程边值问题的多重解 |
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| 引用本文： | 贺铁山,陈文革. 离散广义Emden-Fowler方程边值问题的多重解[J]. 工程数学学报, 2010, 27(1) |
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| 作者姓名： | 贺铁山 陈文革 |
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| 作者单位： | 仲恺农业工程学院计算科学系,广州,510225;华南理工大学数学系,广州,510640 |
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| 基金项目： | 仲恺农业工程学院科研资助项目(G3081724);;广州市科技计划项目(2006J1-C0341)~~ |
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| 摘 要： | 本文研究了离散广义Emden-Fowler方程边值问题多重解的存在性。通过将这类边值问题的解转化为定义在一个适当空间上泛函的临界点,并利用Morse理论中的三临界点定理,文中得到了该问题存在3个解的充分条件,并举例说明了所获得的主要结果是有效的。
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| 关 键 词： | 离散广义Emden-Fowler方程 边值问题 多重解 |
Multiple Solutions to Boundary Value Problems of the Generalized Discrete Emden-Fowler Equation |
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| HE Tie-shan,CHEN Wen-ge. Multiple Solutions to Boundary Value Problems of the Generalized Discrete Emden-Fowler Equation[J]. Chinese Journal of Engineering Mathematics, 2010, 27(1) |
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| Authors: | HE Tie-shan CHEN Wen-ge |
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| Affiliation: | 1- Department of Computation Science;Zhongkai University of Agriculture and Engineering;Guangzhou 510225;2- Department of Mathematics;South China University of Technology;Guangzhou 510640 |
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| Abstract: | In this paper,we investigate the existence of multiple solutions to boundary value problems of the generalized discrete Emden-Fowler equation.By converting solutions of the problems into the critical points of a functional defined on a proper space,some sufficient conditions for the existence of three solutions are obtained by using a three critical points theorem in the Morse theory.Two examples are given to illustrate the effectiveness of the obtained results. |
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| Keywords: | generalized discrete Emden-Fowler equation boundary value problem critical points |
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