Solutions of periodic boundary value problems for second-order nonlinear differential equations via variational methods

By introducing a variational framework for a class of second order nonlinear differential equations with non-separated periodic boundary value conditions, some results on the existence of non-trivial, positive and negative solutions of the problems are obtained. Some results by Atici–Guseinov, Graef–Kong, etc. obtained by topological degree methods are extended. The resonant case of the problems where the nonlinearities are unbounded and satisfy Ahmad–Lazer–Paul type conditions is also considered.