Construction of bubbling solutions for critical biharmonic problems with critical or non-critical perturbation

We study the existence of bubbling solutions of the critical biharmonic problem with Navier boundary condition [Formula: see text] where [Formula: see text] is a smooth function, [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text] is a smooth bounded domain in [Formula: see text], [Formula: see text]. More precisely, we obtain the existence of bubbling solutions concentrating at a single point in [Formula: see text]. In the non-critical perturbation case [Formula: see text], the location of the concentrating point is closely related to the Robin function and the perturbed function [Formula: see text]. However, the location of the concentrating point is determined by the critical point of [Formula: see text] in the critical perturbation case [Formula: see text].