| Abstract: |
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{\bf Abstract}
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In this paper, we study the existence and concentration of positive
solution of a class of coupled Schr\odinger equations. We admit
that the potentials may not be non-negative and suppose that the
intersection of the sets has positive Lebesgue measure. By studying
the modified functional of the associated functional carefully, we
establish the existence of positive least energy solutions for the
coupled Schr\odinger system. Moreover, we prove the concentration
phenomenon of the
positive solution when the parameter goes to infinity.\
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