  In this paper, we consider a critical Grushin-type problem, which is closely
related to the prescribed Webster scalar curvature problems on the CR sphere
with cylindrically symmetric curvature. We first prove a non-degeneracy result
through local Pohozaev identities, then by using the Lyapunov-Schmidt reduction
methods, we construct new type of multi-bubbling solutions with cylindrical
symmetry.
