The Neumann problem for ODEs with indefinite weight: existence and multiplicity

We discuss some recent existence and multiplicity results for the Neumann boundary value problem associated to a wide class of second order nonlinear ordinary differential equations with indefinite weight. The proofs mainly rely on an elementary shooting approach, based on a careful analysis of the trajectories of the solutions in the phase-plane. Joint work with Fabio Zanolin (University of Udine).