科研之友
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摘要
We consider the multi-bump solutions of the following fractional Nirenberg problem @@@ (-Delta)s u = K(x)u(n+2s/n-2s), u > 0 in R-n, @@@ where s is an element of (0, 1) and n > 2 + 2s. If K is a periodic function in some k variables with 1 <= k < n-2s/2, we proved that (0.1) has multi-bump solutions with bumps clustered on some lattice points in R-k 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 R-n which is isomorphic to Z(+)(k).
