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For a radial initial data $u_0\\in H^1(\\mathbb{R}^N)$ under a certain smallness condition we prove that the corresponding solution is global and scatters. The smallness condition is related to the ground state solution of $-Q+\\Delta Q+ |x|^{-b}|Q|^{\\alpha}Q=0$ and the critical Sobolev index $s_c=\\frac{N}{2}-\\frac{2-b}{\\alpha}$. 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Guzm\\'an, Luiz Gustavo Farah","submitted_at":"2017-03-31T17:14:57Z","abstract_excerpt":"We consider the inhomogeneous nonlinear Schr\\\"odinger equation $$ i u_t +\\Delta u+|x|^{-b}|u|^\\alpha u = 0, $$ where $\\frac{4-2b}{N}<\\alpha<\\frac{4-2b}{N-2}$ (when $N=2$, $\\frac{4-2b}{N}<\\alpha<\\infty$) and $0<b<\\min\\{N/3,1\\}$. For a radial initial data $u_0\\in H^1(\\mathbb{R}^N)$ under a certain smallness condition we prove that the corresponding solution is global and scatters. The smallness condition is related to the ground state solution of $-Q+\\Delta Q+ |x|^{-b}|Q|^{\\alpha}Q=0$ and the critical Sobolev index $s_c=\\frac{N}{2}-\\frac{2-b}{\\alpha}$. 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