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Souto, Romildo N. de Lima","submitted_at":"2015-09-17T15:35:38Z","abstract_excerpt":"In this paper, we study the existence of solution for the following class of nonlocal problem, $$ \\left\\{ \\begin{array}{lcl} -\\Delta u=\\left(\\lambda f(x)-\\int_{\\R^N}K(x,y)|u(y)|^{\\gamma}dy\\right)u,\\quad \\mbox{in} \\quad \\R^{N}, \\\\ \\displaystyle \\lim_{|x| \\to +\\infty}u(x)=0,\\quad u>0 \\quad \\text{in} \\quad \\R^{N}, \\end{array} \\right. \\eqno{(P)} $$ where $N\\geq3$, $\\lambda >0, \\gamma\\in[1,2)$, $f:\\R\\rightarrow\\R$ is a positive continuous function and $K:\\R^N\\times\\R^N\\rightarrow\\R$ is a nonnegative function. 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