一类半正奇异Sturm-Liouville边值问题的正解

Solutions for a Class of Singular Semipositone Sturm-Liouville Boundary Value Problem

本文讨论了一类半正奇异Sturm-Liouville边值问题正解的存在性,其中非线性项f(t,u)关于t=0,1和u=0奇异.在非线性项可取负值且下方无界的情形下,利用不动点指数理论以及线性算子的特征值理论得到了该问题正解存在性结果.

In this paper, we studied the existence of positive solutions for a class of semipositone singular Sturm-Liouville boundary value problem, f（t, u） is singular at t =0, 1 and u = 0. With the assumption that f is neither nonnegative nor below bounded, we obtained the existence of the positive solutions by using the theory about fixed point index and the theory about the eigenvalue of linear operators.