A class of modified nonlinear fourth-order elliptic equations with unbounded potential

This paper is concerned on the fourth-order elliptic equation Delta(2)u - Delta u + V(x)u - lambda Delta[rho(u(2))]rho'(u(2))u = f (u) in R-N, u is an element of W-2,W-2(R-N), (P-lambda) where Delta(2) = Delta(Delta) is the biharmonic operator, 3 <= N <= 6, the radially symmetric potential V may change sign and inf(RN) V(x) = -infinity is allowed. If f satisfies a type of nonquadracity and monotonicity conditions and rho is a suitable smooth function, we prove, via variational approach, the existence of a radially symmetric nontrivial ground state solution u. for problem (P-lambda) for all lambda >= 0.