Geodesic
On the number of positive solutions of singularly perturbed 1D NLS
Journal of the European Mathematical Society, Tome 8 (2006) no. 2, pp. 253-268.

Voir la notice de l'article provenant de la source EMS Press

We study singularly perturbed 1D nonlinear Schrödinger equations (1.1). When V(x) has multiple critical points, (1.1) has a wide variety of positive solutions for small ε and the number of positive solutions increases to ∞ as ε→0. We give an estimate of the number of positive solutions whose growth order depends on the number of local maxima of V(x). Envelope functions or equivalently adiabatic profiles of high frequency solutions play an important role in the proof.
DOI : 10.4171/jems/51
Classification : 35-XX, 00-XX
Keywords: Nonlinear Schrödinger equations, singular perturbations, adiabatic profiles 
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     title = {On the number of positive solutions of singularly perturbed {1D} {NLS}},
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Patricio A. Felmer; Salomé Martínez; Kazunaga Tanaka. On the number of positive solutions of singularly perturbed 1D NLS. Journal of the European Mathematical Society, Tome 8 (2006) no. 2, pp. 253-268. doi : 10.4171/jems/51. http://geodesic.mathdoc.fr/articles/10.4171/jems/51/

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