一个半正Sturm-Liouville边值问题的n个解的存在性

通过构造与非线性项有关的辅助函数并考察这个辅助函数在有界集上的性质，对于Sturm-Liouville边值问题建立了几个解的存在性，其中非线性项是下有界的．同时，给出了正解和非平凡解的一个判别方法．主要工具是锥压缩与锥拉伸型的Krasnosel’skii不动点定理．

Existence of n Solutions to a Semipositone Sturm-Liouville Boundary Value Problem

By constractting an auxiliary function concerned with nonlinear term and considering the properties of this auxiliary function on bounded set, the existence of n solutions is established for a Sturm-Liouville boundary value problem, where nonlinear term is lower bounded and n is an arbitrary natural number. And, a discriminatory method of positive solution and nontrivial solution is given. The main ingredient is Krasnosel'skii fixed point theorem of cone expansion-compression type.