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Sreenadh, Tuhina Mukherjee","submitted_at":"2016-11-17T01:46:09Z","abstract_excerpt":"In the present paper, we consider the following magnetic nonlinear Choquard equation $$ \\left\\{\n  \\begin{array}{ll}\n  & (-i \\nabla+A(x))^2u + \\mu g(x)u = \\lambda u + (|x|^{-\\alpha} * |u|^{2^*_\\alpha})|u|^{2^*_\\alpha-2}u ,\\; u>0 \\;\\text{in} \\; \\mathbb{ R}^n ,\n  & u \\in H^1(\\mathbb{R}^n, \\mathbb{ C})\n  \\end{array} \\right\\}.$$ where $n \\geq 4$, $2^*_\\alpha= \\frac{2n-\\alpha}{n-2}$, $\\lambda>0$, $\\mu \\in \\mathbb{ R}$ is a parameter, $\\alpha \\in (0,n)$, $A(x): \\mathbb{R}^n \\rightarrow \\mathbb{ R}^n$ is a magnetic vector potential and $g(x)$ is a real valued potential function on $\\mathbb{R}^n$. 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