奇异二阶微分系统Neumann边值问题的多重正解  

Multiplicity of Positive Solutions to Second Order Singular Neumann Boundary Value Problems of Differential Systems

作　　者：张丽颖[1] 王丽颖[2] 李晓月[3] 

机构地区：[1]健雄职业技术学院基础教学部,太仓215400 [2]吉林白城师范学院数学系,白城137000 [3]东北师范大学数学与统计学院,长春130024

出　　处：《应用数学学报》2008年第6期1035-1045,共11页Acta Mathematicae Applicatae Sinica

基　　金：国家自然科学基金(10571021);东北师范大学自然科学青年基金(20050102)资助项目

摘　　要：本文研究了奇异二阶微分系统Neumann边值问题的多重正解,证明了在适当的条件下该问题至少存在两个解.其中第一个正解的存在性应用了非线性Leray-Schauder抉择定理,第二个解用到了Kras- noselskii锥不动点定理.This paper is devoted to establish the multiplicity of positive solutions to secondorder singular Neumann boundary value problems of differential systems. It is proved that such a problem has at least two positive solutions under our reasonable conditions. The existence of the first solution is obtained by using a nonlinear alternative of Leray-Schauder, and the second one is found by using a Krasnoselskii fixed point theorem ;n

关 键 词：奇异 NEUMANN边值问题 正解 Leray-Schauder抉择 锥不动点定理 

分 类 号：O175.08[理学—数学]