Multiple solutions to fourth-order elliptic problems with steep potential well

Abstract

In this article, we are concerned with a class of fourth-order elliptic equations with sublinear perturbation and steep potential well. By using variational methods, we obtain that such equations admit at least two nontrivial solutions. We also explore the phenomenon of concentration of solutions.

Keywords

• Fourth-order elliptic equations
• variational methods
• critical point
• concentration