We establish the existence of positive radial solutions for the boundary value problems \left\{ \begin{array}{rcll} -\Delta _{p}u&=&\lambda f(u)&\text{ in }B, \\ u&=&0&\text{ on }\partial B, \end{array} \right. where \Delta _{p}u=\textbf{div}(|\nabla u|^{p-2}\nabla u),p\geq 2 , B is the open unit ball \mathbb{R}^{N} , \lambda is a positive parameter, and f:(0,\infty )\rightarrow \mathbb{R} is p -superlinear at \infty and is allowed to be singular at 0 .