Positive solutions for semipositone (k, n-k) conjugate boundary value problems

For 1 less than or equal to k less than or equal to n - 1, positive solutio ns are obtained for the boundary value problem (-1)((n-k))y((n)) = lambdaf(x, y), x is an element of (0,1) y((i))(0) = 0, 0 less than or equal to i less than or equal to k - 1, y((j))(1) = 0, 0 less than or equal to j less than or equal to n - k - 1, where f(x,y) greater than or equal to -M, and M is a positive constant. We show the existence of positive solutions by using a fixed point theorem in cones. (C) 2000 Academic Press.