一类奇异次线性Sturm-Liouville边值问题

A class of singular sublinear Sturm-Liouville boundary value problems

研究了一类次线性Sturm-Liouville边值问题的正解,其中允许非线性项f(t,u)在t=0,t=1和u=0处奇异。主要工具是相关线性问题的Green函数及相应的Hammerstein积分方程。通过考察非线性项在u=0和u=+∞处的增长特性并且利用锥上的Guo-Krasnosel’skii不动点定理证明了一个新的存在定理。

The positive solution is studied for a class of sublinear Sturm-Liouville boundary value problems,where the nonlinear term f（t,u） is allowed to be singular at t=0,t=1 and u=0.The main tools are the Green function of the related linear problem and the corresponding Hammerstein integral equation.By considering the growth features of the nonlinear term at u=0 and u=＋∞,and applying the Guo-Krasnosel skii fixed point theorem on a cone,a new existence theorem is proved.