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摘要
In this paper, we study the following nonlinear Choquard equation @@@ (-Delta)(s)u+V(x)u=(I-alpha*|u|2 alpha,s*)|u|2 alpha,s*-2u,u is an element of Ds,2(RN), @@@ where s is an element of(0,1), N>2s, 0<alpha<N and 2 alpha,s*=N+alpha N-2s is the critical exponent in the sense of Hardy-Littlewood-Sobolev inequality. We showed that Eq. (0.1) has at least one bound state solution if ||V(x)||LN2s is suitably small, by proving a version to the Fractional operator in RN of the Global Compactness result due to Struwe (see Struwe 1984)
