Abstract
In this paper, we deal with the existence and multiplicity of solutions for fourth-order elliptic equations of Kirchhoff type with critical nonlinearity: −ε4Δ2u+ε4a+b∫RN∇u2dxΔu+V(x)u=u2**−2u+h(x,u), (t, x) ∈ ℝ × ℝN. By using Lions’ second concentration-compactness principle and concentration-compactness principle at infinity to prove that (PS) condition holds locally and by variational method, we prove that it has at least one solution and for any m ∈ ℕ, it has at least m pairs of solutions.
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