JournalsaihpcVol. 19, No. 3pp. 261–280

On the number of single-peak solutions of the nonlinear Schrödinger equation

  • Massimo Grossi

    Dip. di Matematica, Università di Roma “La Sapienza”, P. le A.Moro 2, 00185 Roma, Italy
On the number of single-peak solutions of the nonlinear Schrödinger equation cover
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Abstract

In this paper we consider uniqueness and multiplicity results for single-peak solutions for the nonlinear Schrödinger equation. For a suitable class of potentials V and critical points P we are able to establish exact multiplicity results. In particular we show that for any nondegenerate critical point of V there are only one solution concentrating at P. Moreover some examples of single-peak solutions concentrating at the same point P are provided.

Résumé

Dans ce papier nous considérons les résultats d'unicité et de multiplicité pour les solutions de seul-pic pour l'équation de Schrödinger non linéaire. Pour une classe convenable de potentiel V et critiques points P nous peuvons établir une multiplicité exacte.

Cite this article

Massimo Grossi, On the number of single-peak solutions of the nonlinear Schrödinger equation. Ann. Inst. H. Poincaré Anal. Non Linéaire 19 (2002), no. 3, pp. 261–280

DOI 10.1016/S0294-1449(01)00089-0