Abstract
In this paper, we study the following nonlinear Choquard equation
where \(s\in (0,1)\), \(N>2s\), \(0<\alpha <N\) and \(2^{*}_{\alpha ,s}=\frac{N+\alpha }{N-2s}\) 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 \(\Vert V(x)\Vert _{L^{\frac{N}{2s}}}\) is suitably small, by proving a version to the Fractional operator in \(\mathbb {R}^N\) of the Global Compactness result due to Struwe (see Struwe 1984)
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Acknowledgements
The author would like to thank Professor Yinbin Deng very much for stimulating discussions and helpful suggestions on the present paper. The research of X. L. Yang was supported by the graduate education innovation funding [Grant number 2019CXZZ082] from Central China Normal University.
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Communicated by José Tenreiro Machado.
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Yang, X. Bound state solutions of fractional Choquard equation with Hardy–Littlewood–Sobolev critical exponent. Comp. Appl. Math. 40, 171 (2021). https://doi.org/10.1007/s40314-021-01559-7
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DOI: https://doi.org/10.1007/s40314-021-01559-7