INFINITELY MANY SOLUTIONS FOR FOURTH-ORDER ELLIPTIC EQUATIONS WITH SIGN-CHANGING POTENTIAL

Abstract

In this paper, we study the following fourth-order elliptic equation $$ \left\{ \begin{array}{ll} \Delta^{2}u-\Delta u+V(x)u=f(x, u), \ \ \ x\in\mathbb{R}^{N},\\ u\in H^{2}(\mathbb{R}^{N}), \end{array} \right. $$ where the potential $V\in C(\mathbb{R}^N, \mathbb{R})$ is allowed to be sign-changing. Under the weakest superquadratic conditions, we establish the existence of infinitely many solutions via variational methods for the above equation. Recent results from the literature are extended.