Abstract:

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=1and u=0.The main tools are the Green function of the related linear problem and the corresponding Hammerstein integral equation. By nsidering 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

Key words: singular ordinary differential equation; Sturm-Liouville boundary value problem; positive solution; existence theorem