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Sreenadh, Tuhina Mukherjee","submitted_at":"2016-05-22T15:32:23Z","abstract_excerpt":"In this article, we study the Brezis-Nirenberg type problem of nonlinear Choquard equation involving a fractional Laplacian \\[ (-\\De)^s u = \\left( \\int_{\\Om}\\frac{|u|^{2^*_{\\mu,s}}}{|x-y|^{\\mu}}\\mathrm{d}y \\right)|u|^{2^*_{\\mu,s}-2}u +\\la u \\; \\text{in } \\Om,\\] where $\\Om $ is a bounded domain in $\\mathbb R^n$ with Lipschitz boundary, $\\la $ is a real parameter, $s \\in (0,1)$, $n >2s$ and $2^*_{\\mu,s}= (2n-\\mu)/(n-2s)$ is the critical exponent in the sense of Hardy-Littlewood-Sobolev inequality. 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