Nontrivial solutions and least energy nodal solutions for a class of fourth-order elliptic equations

摘要

This paper is concerned with the following fourth-order elliptic equation {?~2u - ?u + V(x)u = |u|~(p-1)u, in R~N, u ∈ H~2 (R~N), where p ∈ (2, 2_*-1), u:R~N → R. Under some appropriate assumptions on potential V(x), the existence of nontrivial solutions and the least energy nodal solution are obtained by using variational methods.