On singular Sturm-Liouville boundary-value problems

We consider the existence of positive solutions for the boundary-value problem (q(t)phi(u'))' + lambda f (t, u) - 0, r < t < R, au(r) - b phi(-1)(q(r))u'(r) = 0, cu(R) + d phi(-1) (q(R))u'(R) = 0, where phi(u') = vertical bar u'vertical bar(p-2)u', p > 1, lambda > 0, f is p-superlinear or p-sublinear at infinity and is allowed to become -infinity at u = 0. Our results unify and extend many known results in the literature.