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

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.

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.