Existence of positive solutions for singular ordinary differential equations with nonlinear boundary conditions

We prove the existence of nonnegative solutions of the problem $(py')'/p+\mu qg(x,y)=0$, $\lim _{x\to 0+}py'=0$, $h(y'(1))+y(1)=0$ for a physically motivated class of nonlinearity $h$. The results, which are established using a ``forbidden value'' argument, are new even in the case of linear $h$.