Infinitely many solutions for fourth-order elliptic equations with general potentials

Abstract

This paper is concerned with the following fourth-order elliptic equations {Δ2u−Δu+V(x)u=f(x,u)in RN,u∈H2(RN), where u:RN→R. Under general assumption on potential V(x), and f(x,u) is indefinite sign and sublinear as |u|→∞, we establish the existence of infinitely many solutions by using the genus properties in critical point theory. Recent results from the literature are extended.