Ground states for a class of asymptotically linear fourth-order elliptic equations

摘要

this paper, we study the following fourth-order elliptic equation, { Delta(2)u - Delta u + V(x)u = f (x,u), x epsilon R-N, u epsilon H-2(R-N), where Delta(2) := Delta(Delta) is the biharmonic operator, V epsilon C(R-N) and f epsilon C(R-N x R). We apply the variational methods to obtain the existence of ground-state solutions for asymptotically linear case.