Infinitely many non-radial solutions for fractional Nirenberg problem

In this paper, the prescribed (sigma )-curvature problem

$$begin{aligned} P_{sigma }^{g_0} u={tilde{K}}(x)u^{frac{N+2sigma }{N-2sigma }}, xin {mathbb {S}}^N,u>0 end{aligned}$$

is considered. When ({tilde{K}}(x)) is some axis symmetric function on ({mathbb {S}}^N), by using singular perturbation method, it is proved that this problem possesses infinitely many non-radial solutions for (0 2sigma +2).