In this paper we consider the existence of positive solutions to the boundary-value problems (p(t)u')'−q (t) u+λf(t, u) = 0, r<t<R, au(r)−bp(r)u'(r) =m−2Σi=1αiu(ξi), cu(R) + dp(R)u'(R) =m−2Σt=1βiu(ξi), where λ is a positive parameter, a, b, c, d ∈ [0,∞], ξi ∈ (r,R), αi, βi ∈ [0,∞] (for i ∈ {1,... m − 2}) are given constants satisfying some suitable conditions. Our results extend some of the existing literature on superlinear semipositone problems. The proofs are based on the fixed-point theorem in cones.