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Miyagaki","submitted_at":"2015-06-22T10:06:58Z","abstract_excerpt":"In this paper, we study the existence of positive solution for the following class of fractional elliptic equation $$ \\epsilon^{2s} (-\\Delta)^{s}{u}+V(z)u=\\lambda |u|^{q-2}u+|u|^{2^{*}_{s}-2}u\\,\\,\\, \\mbox{in} \\,\\,\\, \\mathbb{R}^{N}, $$ where $\\epsilon, \\lambda >0$ are positive parameters, $q \\in (2,2^{*}_{s}), 2^{*}_{s}=\\frac{2N}{N-2s}, $ $N > 2s,$ $s \\in (0,1),$ $ (-\\Delta)^{s}u$ is the fractional laplacian, and $V$ is a saddle-like potential. The result is proved by using minimizing method constrained to the Nehari manifold. 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