二阶奇异非线性特征值问题正解的存在性  

Existence of positive solutions of second order singular nonlinear eigenvalue problems

作　　者：曹文娟 李杰梅 温九红 CAO Wen-Juan;LI Jie-Mei;WEN Jiu-Hong(School of Mathematics and Physics,Lanzhou Jiaotong University,Lanzhou 730070,China)

机构地区：[1]兰州交通大学数理学院,兰州730070

出　　处：《四川大学学报（自然科学版）》2018年第6期1148-1154,共7页Journal of Sichuan University(Natural Science Edition)

基　　金：甘肃省自然科学基金(1308RJZA113);甘肃省高校基本科研业务费基金(212084)

摘　　要：本文讨论了含一般微分算子的二阶奇异微分方程在Sturm-Liouville边值条件下的正解的存在性.通过将非线性项f在原点及无穷远处的增长性分为9种情形,本文运用锥拉伸与压缩不动点定理获得了问题无正解、至少有一个正解及至少有两个正解存在时参数λ的取值范围.In this paper, we consider the existence of positive solutions for the second-order singular differential equation with Sturm-Liouville boundary condition. By dividing the growth property of f at zero and infinity into 9 cases, we discuss the ranges of λ corresponding to the cases of the equation having none, at least one and two positive solutions by using the fixed point theorem of cone expansion and compression.

关 键 词：二阶奇异微分方程 不动点定理 正解 Sturm-Liouville边值条件 

分 类 号：O175.8[理学—数学]