Multiplicity results to a fourth-order boundary value problem for a Sturm-Liouville type equation

Abstract

We establish the existence of at least three distinct weak solutions for a fourth-order Sturm-Liouville type problem under appropriate hypotheses. Our main tools are based on variational methods and some critical points theorems. Moreover, when the energy functional is not coercive, an existence result of two distinct solutions is given. We give some examples to illustrate the obtained results.