Journal of the European Mathematical Society

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Volume 10, Issue 1, 2008, pp. 47–71
DOI: 10.4171/JEMS/103

Semiclassical states for weakly coupled nonlinear Schrödinger systems

Eugenio Montefusco[1], Benedetta Pellacci[2] and Marco Squassina[3]

(1) Dipartimento di Matematica, Università di Roma La Sapienza, Piazzale A. Moro 2, 00185, Roma, Italy
(2) Dipartimento di Scienze Applicate, Università degli Studi di Napoli 'Parthenope', Via De Gasperi 5, 80133, Napoli, Italy
(3) Dipartimento di Matematica e Fisica, Università Cattolica del Sacro Cuore, Via dei Musei 41, 25121, Brescia, Italy

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.

Keywords: Weakly coupled nonlinear Schrödinger systems, concentration phenomena, semiclassical limit, ground states, critical point theory, Clarke's subdifferential

Montefusco Eugenio, Pellacci Benedetta, Squassina Marco: Semiclassical states for weakly coupled nonlinear Schrödinger systems. J. Eur. Math. Soc. 10 (2008), 47-71. doi: 10.4171/JEMS/103