离散广义Emden-Fowler方程边值问题的多重解  

Multiple Solutions to Boundary Value Problems of the Generalized Discrete Emden-Fowler Equation

作　　者：贺铁山[1] 陈文革[2] 

机构地区：[1]仲恺农业工程学院计算科学系,广州510225 [2]华南理工大学数学系,广州510640

出　　处：《工程数学学报》2010年第1期145-151,共7页Chinese Journal of Engineering Mathematics

基　　金：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)~~

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。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.

关 键 词：离散广义Emden—Fowler方程 边值问题 多重解 

分 类 号：O175.7[理学—数学]