A sharp existence and localization theorem for a Neumann problem

摘要

We shall present a new version of a recently appeared theorem for the existence and localization of solutions of the Neumann problem associated to the equation -u"+u = β(t)g(u), based on a general variational principle by Ricceri. Our study will be especially aimed to express a certain hypothesis regarding the function g in its sharpest form, and a limit case is enquired by an approximation.