Abstract
In this article, we study the Brezis–Nirenberg type problem of nonlinear Choquard equation involving the fractional Laplacian
where \(\Omega \) is a bounded domain in \(\mathbb R^n\) with Lipschitz boundary, \(\lambda \) is a real parameter, \(s \in (0,1)\), \(n >2s\), \(0<\mu <n\) and \(2^*_{\mu ,s}= (2n-\mu )/(n-2s)\) is the critical exponent in the sense of Hardy–Littlewood–Sobolev inequality. We obtain some existence, nonexistence and regularity results for weak solution of the above problem using variational methods.
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Mukherjee, T., Sreenadh, K. Fractional Choquard equation with critical nonlinearities. Nonlinear Differ. Equ. Appl. 24, 63 (2017). https://doi.org/10.1007/s00030-017-0487-1
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DOI: https://doi.org/10.1007/s00030-017-0487-1