Existence of Multi-bubbling Solutions for a Class of Fractional Prescribed Curvature Problems
We consider the following prescribed curvature problem of fractional op-erator:(-Δ)su=K(y)u2*s-1,u＞0,u∈Ds(RN),where N≥3,0＜s＜1,2*s=2N/N-2s is the fractional critical Sobolev exponent,K(y)is a positive function.When K(y)has a sequence of strictly local maximum points moving to infinity,we use the finite dimensional reduction method to prove the existence of any finitely many multi-bubbling solutions to the above problem.These solutions concentrate at k different local maximum points of K(y).
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