The paper deals with the existence of multiple positive solutions for the boundary value problem (ϕ(p(t)u (n−1))(t))′ + a(t)f(t, u(t), u′ (t), . . . , u(n−2)(t)) = 0, 0 < t < 1, u (i) (0) = 0, i = 0, 1, . . . , n − 3, u (n−2)(0) = mP−2 i=1 αiu (n−2)(ξi), u(n−1)(1) = 0, where ϕ: R → R is an increasing homeomorphism and a positive homomorphism with ϕ(0) = 0. Using a fixed-point theorem for operators on a cone, we provide sufficient conditions for the existence of multiple positive solutions to the above boundary value problem.