奇异超线性方程周期边值问题多重正解的存在性  

Existence of Multiplicity of Positive Solutions to Singular Superlinear Equations with Periodic Boundary Value Problems

作　　者：张丽娟[1] 蒋达清[2] 田颖辉[3] 

机构地区：[1]白城师范学院数学系,吉林白城137000 [2]东北师范大学数学与统计学院,长春130024 [3]阜新高等专科学校数学系,辽宁阜新123000

出　　处：《吉林大学学报（理学版）》2009年第3期487-491,共5页Journal of Jilin University:Science Edition

基　　金：国家自然科学基金(批准号:10571021)

摘　　要：研究具有奇异超线性周期边值问题多重正解的存在性,利用非线性Leray-Schauder抉择定理和Krasnoselskii锥不动点定理,证明了在一定条件下,且非线性项具有奇异和超线性时,此问题至少存在两个正解.This paper deals with the multiplicity of positive solutions to singular superlinear equations with periodic boundary value problems. It is proved that such a problem has at least two positive solutions under our reasonable conditions when the nonlinear term possesses singularity and super-linearity. The proof relies on a nonlinear alternative of Leray-Schauder theorem and Krasnoselskii on fixed point theorem in cones.

关 键 词：周期边值问题 奇异超线性方程 周期解 Leray-Schauder抉择定理 Krasnoselskii锥不动点定理 

分 类 号：O175[理学—数学]