A variational approach to a discrete fourth-order boundary value problem with three parameters

Abstract

In this article, we study
discrete nonlinear fourth order boundary value problems with three parameters. We establish the
existence of at least one solution under an asymptotical behaviour of
the potential of the nonlinear term at zero by using variational methods. Some recent results
are extended and improved. We provide sufficient
conditions for the existence of positive solutions. An example is presented to
demonstrate the applications of our main results.