AbstractThis paper is concerned with the existence of two nontrivial positive solutions to a class of boundary value problems involving a p-Laplacian of the form where Φp(x) = |x| p−2x is a one dimensional p-Laplacian operator with p > 1, a and b are real constants, and α and β are given by the Riemann-Stieltjes integrals with A and B functions of bounded variation. The approach used is based on fixed point index theory. The results obtained in this paper are new in the literature.