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(兰州交通大学数理学院)；李杰梅(兰州交通大学数理学院)；温九红(兰州交通大学数理学院)

Author：CAO Wen-Juan(School of Mathematics and Physics, Lanzhou Jiaotong University)；LI Jie-Mei(School of Mathematics and Physics, Lanzhou Jiaotong University)；WEN Jiu-Hong(School of Mathematics and Physics, Lanzhou Jiaotong University)

收稿日期：2018-04-08 年卷（期）页码：2018,55(6):1148-1154

期刊名称：四川大学学报: 自然科学版

Journal Name：Journal of Sichuan University (Natural Science Edition)

关键字：二阶奇异微分方程；不动点定理; 正解; Sturm-Liouville边值条件

Key words：Second-order singular differential equation; Fixed point theorem; Positive solution; Sturm-Liouville boundary condition

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

中文摘要

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在原点和无穷远处的增长性分九种情形,本文运用锥拉伸与压缩不动点定理获得了所讨论问题无正解、至少一个或两个正解存在的参数的取值范围.

英文摘要

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 range of parameter 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.

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论文摘要

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