Indefinite Fourth Order Elliptic Equations with Decay or Integrable Weights

We consider fourth order elliptic equations in \(R^N\) of the form \[Δ^2u-Δ u+V(x)u-1/2uΔ(u^2)=f(x,u),\] where the operator \(Δ^2-Δ+V\) is allowed to be indefinite. We study the case that the potential \(V\) is bounded so that the working space is \(H^2(R^N)\), which can not be compactly embedded into Lebesgue spaces. To overcome this difficulty, the nonlinearity considered here satisfies decay or integrable weights. By local linking theorem, we obtain a nontrivial solution for the problem.