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Sreenadh, Tuhina Mukherjee","submitted_at":"2016-02-25T11:18:37Z","abstract_excerpt":"In this article, we study the following fractional Laplacian equation with critical growth and singular nonlinearity  $$\\quad (-\\Delta)^s u = \\lambda a(x) u^{-q} + u^{2^*_s-1}, \\quad u>0 \\; \\text{in}\\; \\Omega,\\quad u = 0 \\; \\mbox{in}\\; \\mathbb{R}^n \\setminus\\Omega,$$ where $\\Omega$ is a bounded domain in $\\mathbb{R}^n$ with smooth boundary $\\partial \\Omega$, $n > 2s,\\; s \\in (0,1),\\; \\lambda >0,\\; 0 < q \\leq 1 $, $\\theta \\leq a(x) \\in L^\\infty(\\Omega)$, for some $\\theta>0$ and $2^*_s=\\frac{2n}{n-2s}$. 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Sreenadh, Tuhina Mukherjee","submitted_at":"2016-02-25T11:18:37Z","abstract_excerpt":"In this article, we study the following fractional Laplacian equation with critical growth and singular nonlinearity  $$\\quad (-\\Delta)^s u = \\lambda a(x) u^{-q} + u^{2^*_s-1}, \\quad u>0 \\; \\text{in}\\; \\Omega,\\quad u = 0 \\; \\mbox{in}\\; \\mathbb{R}^n \\setminus\\Omega,$$ where $\\Omega$ is a bounded domain in $\\mathbb{R}^n$ with smooth boundary $\\partial \\Omega$, $n > 2s,\\; s \\in (0,1),\\; \\lambda >0,\\; 0 < q \\leq 1 $, $\\theta \\leq a(x) \\in L^\\infty(\\Omega)$, for some $\\theta>0$ and $2^*_s=\\frac{2n}{n-2s}$. 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