二阶常微分方程Neumann边值问题正解的全局分歧  

Global Bifurcation of Positive Solutions of Neumann Boundary Value Problems for Second-order O.D.E.

作　　者：陈瑞鹏[1] 马如云[1] 闫东明[2] 

机构地区：[1]西北师范大学数学与信息科学学院,兰州730070 [2]四川大学数学学院,成都610064

出　　处：《应用数学学报》2012年第3期515-528,共14页Acta Mathematicae Applicatae Sinica

基　　金：国家自然科学基金(11061030)资助项目

摘　　要：本文考虑二阶常微分方程Neumann边值问题正解的存在性,其中f:[0,1]×R→R(R=(-∞,+∞))为连续函数.运用Dancer全局分歧定理建立了上述问题正解的全局分歧,并且获得了保证上述问题存在正解的若干最优充分条件.In this paper, we are concerned with the existence of positive solutions of the following second-order Neumann boundary value problem{u^ll=f（t,u）,t∈（0,1）,u^l（0）=0,u^l（1）=0 where f[0,1]×R→R（R=（-∞＋∞））is continuous. By using Dancer＇s global bifurca-tion theorem, we estabish the global bifurcation of positive solutions of the above problem. Moreover, we obtain several optimal sufficient conditions which guarantee that the above problem has at least one positive solution.

关 键 词：NEUMANN边值问题 Dancer全局分歧定理 正解 最优条件 

分 类 号：O175.8[理学—数学]