The existence of positive solution was studied for the

nonlinear Sturm-Liouville boundary value problem, where the

nonlinear term $f(t,u)$ may be singular at $t = 0,\,t = 1$. By

introducing the integrations of height functions of nonlinear term

on bounded set the growths of nonlinear term were described. By

applying the Krasnoselskii fixed point theorem in degree theory and

the dominated convergence theorems in real variable, an existence

theorem of positive solution was proved when there are limit

functions $\mathop {\lim }\limits_{u \to + 0} f(t,u) / u$ and

$\mathop {\lim }\limits_{u \to + \infty } f(t,u) / u$.