We describe the asymptotic behavior of conformal metrics related to the GJMS operator in the null case, as the prescribed Q-curvature \(f_0(x) + \lambda \) gradually changes. We show that if one of the maximum points of \(f_0\) is flat up to order \(n-1\) , the normalized conformal metrics in the lowest energy level will form exactly one spherical bubble as \(\lambda \) approaches zero using higher order Bol’s inequality. This generalizes the result of Struwe (J Eur Math Soc 22:3223-3262, 2020) in the two-dimensional case to higher dimensions and helps rule out the slow bubble case discussed by Ngô and Zhang (Bubbling of the prescribed Q-curvature equation on 4-manifolds in the null case. arXiv:1903.12054) to some degree.
