Singular differential equations with (n,p) boundary conditions

We offer criteria for the existence of a positive solution of the boundary value problem y(n) + ƒ (t, y, y′, …, y(p) = 0, tϵ (0, 1), y(i)(0) = 0, 0 ≤ i ≤ n — 2, y(p)(1) = 0, where 0 ≤p ≤ n — 1 is a fixed integer, and the function ƒ(t,u0,u1,…,up) is singular at uj = 0, 0 ≤ j ≤ p. The technique used involves an application of topological transversality theory.