Eigenvalue characterization for (n,p) boundary-value problems

We consider the (n, p) boundary value problem y((n)) + lambda H(t, y) = lambda K(t, y), n greater than or equal to 2, t is an element of (0, 1), y((p)) (1) = y((i))(0) = 0, 0 less than or equal to i less than or equal to n - 2, where lambda > 0 and 0 p less than or equal to n - 1 is fixed. We characterize the values of lambda such that the boundary value problem has a positive solution. For the special case lambda = 1, we also offer sufficient conditions for the existence of positive solutions of the boundary value problem.