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

摘要

In this paper, we study the following fourth-order elliptic equation {Δ~2u ? Δu + V (x)u = f(x, u), x∈ R~N, u ∈ H~2(R~N), where the potential V ∈ C(R~N,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.