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Germano","submitted_at":"2018-01-24T18:26:51Z","abstract_excerpt":"In this paper we are interested to prove the existence and concentration of ground state solution for the following class of problems $$ -\\Delta u+V(x)u=A(\\epsilon x)f(u), \\quad x \\in \\R^{N}, \\eqno{(P)_{\\epsilon}} $$ where $N \\geq 2$, $\\epsilon>0$, $A:\\R^{N}\\rightarrow\\R$ is a continuous function that satisfies $$ 0<\\inf_{x\\in\\R^{N}}A(x)\\leq\\lim_{|x|\\rightarrow+\\infty}A(x)<\\sup_{x\\in\\R^{N}}A(x)=A(0),\\eqno{(A)} $$ $f:\\R\\rightarrow\\R$ is a continuous function having critical growth, $V:\\R^{N}\\rightarrow\\R$ is a continuous and $\\Z^{N}$--periodic function with $0\\notin\\sigma(\\Delta+V)$. 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