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

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.