具有正Green函数的奇异Sturm-Liouville边值问题的正解

Positive Solutions of Singular Sturm-Liouville Boundary Value Problems with Positive Green Function

中文关键词:  奇异常微分方程  Sturm-Liouville边值问题  正解  存在性与多解性.

英文关键词:singular ordinary differential equation  Sturm-Liouville boundary value problem  positive solution  existence and multiplicity.

中文摘要:

      考察了具有正Green函数的奇异Sturm-Liouville边值问题的正解存在性与多解性,其中相对于空间变元非线性项可以是超强奇异的.通过构造适当的控制函数,精确估计了解的先验界.利用锥压缩-拉伸型的Guo-Krasnosel'skii不动点定理,证明了几个存在结论.

英文摘要:

      The existence and multiplicity of positive solutions are studied for a singular Sturm-Liouville boundary value problem with positive Green function, where the nonlinearity may be super-strongly singular with respect to the space variable. By constructing suitable control functions, the a priori bound of solution is exactly estimated. By applying the Guo-Krasnosel'skii fixed point theorem of cone expansion-compression type, several existence results are proved.