Nontrivial Solutions of a Class of Fourth-Order Elliptic Problems with Potentials

Abstract

This paper deals with a fourth-order elliptic equation with Dirichlet boundary conditions. Using a variant form of the mountain pass theorem, we prove the existence of nontrivial solutions to this problem. Furthermore, we discuss the fundamental properties of the representation of the solution by considering two cases. Our results not only make previous results more general but also show new insights into fourth-order elliptic problems.