We consider systems of weakly coupled Schrödinger equations with nonconstant potentials and we investigate the existence of nontrivial nonnegative solutions which concentrate around local minima of the potentials. We obtain sufficient and necessary conditions for a sequence of least energy solutions to concentrate.
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Eugenio Montefusco, Benedetta Pellacci, Marco Squassina, Semiclassical states for weakly coupled nonlinear Schrödinger systems. J. Eur. Math. Soc. 10 (2008), no. 1, pp. 47–71DOI 10.4171/JEMS/103