Non-degeneracy and new type of cylindrial solutions for a critical Grushin-type problem
Abstract
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.
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