Sign‐changing solutions for a nonhomogeneous Paneitz‐type problem

We consider the problemP εΔ 2 u = | u | 8 N − 4u + ε f ( x )in Ω , u = Δ u = 0on ∂ Ω , where Ω is a bounded smooth domain in R N , N ≥ 5 , that exhibits certain symmetries and contains the origin, f ∈ L ∞ ( Ω ) , f ≥ 0 , f ≢ 0 , and ε > 0 is a small parameter. By using the Lyapunov–Schmidt reduction method and topological degree theory, for each sufficiently large k ∈ N , we construct sign‐changing solutions to ( P ε ) exhibiting k negative spikes at the vertices of a regular polygon and a single positive spike at the origin.