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We consider the following fractional prescribed curvature problem$$(-\Delta)^s u= K(y)u^{2^*_s-1},\ \ u>0,\ \ y\in \mathbb{R}^N,\qquad (0.1)$$where $s\in(0,\frac{1}{2})$ for $N=3$, $s\in(0,1)$ for $N\geqslant4$ and$2^*_s=\frac{2N}{N-2s}$ is the fractional critical Sobolev exponent, $K(y)$ hasa local maximum point in $r\in(r_0-\delta,r_0+\delta)$. First, for anysufficient large $k$, we construct a $2k$ bubbling solution to (0.1) of somenew type, which concentrate on an upper and lower surfaces of an oblatecylinder through the Lyapunov-Schmidt reduction method. Furthermore, anon-degeneracy result of the multi-bubbling solutions is proved by use ofvarious Pohozaev identities, which is new in the study of the fractionalproblems.

Infinitely many bubbling solutions and non-degeneracy results to fractional prescribed curvature problems