无穷远分歧的离散周期边值问题的多个解(英文)  

Bifurcation from Infinity and Multiple Solutions for Discrete Periodic Boundary Value Problems

作　　者：马慧莉[1] 马如云[1] 

机构地区：[1]西北师范大学数学系,兰州730070

出　　处：《工程数学学报》2012年第5期773-779,共7页Chinese Journal of Engineering Mathematics

基　　金：The National Natural Science Foundation of China(11126296);the Scientific ResearchPromotion Funds for Young Teachers in Northwest Normal University(SKQNGG10018;NWNU-LKQN-10-1)

摘　　要：本文讨论了一类二阶非线性含参离散周期边值问题多个对称解的存在性.在非线性项次线性增长的条件下,本文确定了参数依赖于共振点的不同取值范围,在不同范围内的参数确保了问题不同个数对称解的存在性,并且指明了这些解的奇偶性.本文使用的主要方法是Leray-Schauder原理和分歧定理.This paper discusses a class of nonlinear second order discrete boundary value problems with parameter. We obtain the multiplicity result of symmetric solution for the problem in the condition that the nonlinear term grows in sublinear state. We determine different number of symmetric solutions of the problem in different range of the parameter near the resonant point, and each of theses solutions has its specific parity. The main methods used in this paper include Leray-Schauder principle and bifurcation theorem.

关 键 词：周期边值问题 特征值 解 分歧 

分 类 号：O175.7[理学—数学]