Weak solutions of quasilinear biharmonic problems with convex nonlin- earities

Abstract

We study the existence of positive weak solutions to a fourth-order semi- linear elliptic equation with Navier boundary conditions and a positive, increasing and convex source term. We also prove the uniqueness of extremal solutions. In particular, we generalize results of Mironescu and R˘adulescu for the bi-Laplacian operator.