中文摘要：

讨论一类奇异二阶常微分方程的非局部边值问题，利用锥上的不动点指数定理，建立问题正解的存在性、不存在性以及多解性的结果。

英文摘要：

The paper is concerned with a nonlocal boundary value problem of second-order singular nonlinear ordinary differential equation. By the use of the fixed-point index theorem in cones, the existence ,non-existence and multiplicity of positive solution（s） are established.