Multiplicity results for fourth order elliptic equations of Kirchhoff-type

In this paper, we concern with the following fourth order elliptic equations of Kirchhoff type {Δ2u-(a+b∫R3|∇u|2dx)Δu=f(x,u),x∈ℝ3,u∈H2(ℝ3), where a,b > 0 are constants and the primitive of the nonlinearity f is of superlinear growth near infinity in u and is also allowed to be sign-changing. By using variational methods, we establish the existence and multiplicity of solutions. Our conditions weaken the Ambrosetti-Rabinowitz type condition.