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.