Multiplicity results for classes of one-dimensional p-Laplacian boundary-value problems with cubic-like nonlinearities

We study boundary-value problems of the type -(phi(p)(u'))' = lambda f(u); in (0, 1) u(0) = u(1) = 0, where p > 1, phi(p) (x) - vertical bar x vertical bar(p-2) x, and lambda > 0. We provide multiplicity results when f behaves like a cubic with three distinct roots, at which it satisfies Lipschitz-type conditions involving a parameter q > 1. We shall show how changes in the position of q with respect to p lead to different behavior of the solution set. When dealing with sign-changing solutions, we assume that f is half-odd; a condition generalizing the usual oddness. We use a quadrature method.