Existence of positive solutions for superlinear semipositone m-point boundary-value problems

In this paper we consider the existence of positive solutions to the boundary-value problems (p(t)u')' - q(t)u + lambdaf(t,u) = 0, r < t < R, au(r) - bp(r)u'(r) = Sigma(i=1)(m-2) alpha(i)u(xi(i)), cu(R) + dp(R)u'(R) = Sigma(i=1)(m-2) beta(i)u(xi(i)), where lambda is a positive parameter, a,b,c,d is an element of [0, infinity), xi(i) is an element of (r, R), alpha(i), beta(i) is an element of [0, infinity) (for i is an element of {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.