| 二阶奇异非线性特征值问题正解的存在性 |
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| 引用本文： | 曹文娟,李杰梅,温九红.二阶奇异非线性特征值问题正解的存在性[J].四川大学学报(自然科学版),2018,55(6):1148-1154. |
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| 作者姓名： | 曹文娟 李杰梅 温九红 |
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| 作者单位： | 兰州交通大学数理学院,兰州交通大学数理学院,兰州交通大学数理学院 |
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| 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) |
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| 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.
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| 关 键 词： | 二阶奇异微分方程 不动点定理 正解 Sturm-Liouville边值条件 |
| 收稿时间： | 2018/4/8 0:00:00 |
| 修稿时间： | 2018/4/27 0:00:00 |
Existence of positive solutions of second order singular nonlinear eigenvalue problems |
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| CAO Wen-Juan,LI Jie-Mei and WEN Jiu-Hong.Existence of positive solutions of second order singular nonlinear eigenvalue problems[J].Journal of Sichuan University (Natural Science Edition),2018,55(6):1148-1154. |
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| Authors: | CAO Wen-Juan LI Jie-Mei and WEN Jiu-Hong |
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| Institution: | School of Mathematics and Physics, Lanzhou Jiaotong University,School of Mathematics and Physics, Lanzhou Jiaotong University,School of Mathematics and Physics, Lanzhou Jiaotong University |
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| Abstract: | 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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| Keywords: | Second-order singular differential equation Fixed point theorem Positive solution Sturm-Liouville boundary condition |
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