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In this paper, we consider the following nonlinear coupled elliptic systems with continuous potentials:{-ε2△u +(1 + δP(x))u = μ1 u3+ βuv2 in Ω,-ε2△v +(1 + δQ(x))v = μ2 v3+ βu2 v in Ω,u > 0, v > 0 in Ω,(?u)/(?v)=(?ν)/(?ν)=0on ?Ω,(Aε)where Ω is a smoo