From the introduction: The authors give an existence result for the Neumann boundary value problem associated to a second-order equation of the form
satisfies the Carathéodory conditions. It is assumed that there exists
, together with a Nagumo-type condition. The authors provide a priori bounds on the
-norm of the (possible) solutions to a parameter-dependent problem associated to the given one; existence is then achieved by using degree arguments (more precisely, the “topological transversality theorem").