Multiplicity Results for Classes of One-dimensional p-Laplacian Boundary-value Problems with Cubic-like Nonlinearities

Abstract

We study boundary-value problems of the type -(φp(x) = |x|p-2 x, and λ > 0. We provide multiplicity results when ƒ 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 ƒ is half-off; a condition generalizing the usual oddness. We use a quadrature method.