Abstract
We consider the multi-bump solutions of the following fractional Nirenberg problem (0.1)(−Δ)su=K(x)un+2sn−2s,u>0inRn,where s∈(0,1) and n>2+2s. If K is a periodic function in some k variables with 1≤k<n−2s2, we proved that (0.1) has multi-bump solutions with bumps clustered on some lattice points in Rk via Lyapunov–Schmidt reduction. It is also established that the (0.1) has an infinite-many-bump solutions with bumps clustered on some lattice points in Rn which is isomorphic to Z+k.
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