# On the number of positive solutions of singularly perturbed 1D nonlinear Schrödinger equations

Patricio Felmer; Salomé Martínez; Kazunaga Tanaka

Journal of the European Mathematical Society (2006)

- Volume: 008, Issue: 2, page 253-268
- ISSN: 1435-9855

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topFelmer, Patricio, Martínez, Salomé, and Tanaka, Kazunaga. "On the number of positive solutions of singularly perturbed 1D nonlinear Schrödinger equations." Journal of the European Mathematical Society 008.2 (2006): 253-268. <http://eudml.org/doc/277367>.

@article{Felmer2006,

abstract = {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 $\varepsilon $ and the number of positive solutions increases to $\infty $ as $\varepsilon \rightarrow 0$. 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.},

author = {Felmer, Patricio, Martínez, Salomé, Tanaka, Kazunaga},

journal = {Journal of the European Mathematical Society},

keywords = {nonlinear Schrödinger equations; singular perturbations; adiabatic profiles; nonlinear Schrödinger equations; singular perturbations; adiabatic profiles},

language = {eng},

number = {2},

pages = {253-268},

publisher = {European Mathematical Society Publishing House},

title = {On the number of positive solutions of singularly perturbed 1D nonlinear Schrödinger equations},

url = {http://eudml.org/doc/277367},

volume = {008},

year = {2006},

}

TY - JOUR

AU - Felmer, Patricio

AU - Martínez, Salomé

AU - Tanaka, Kazunaga

TI - On the number of positive solutions of singularly perturbed 1D nonlinear Schrödinger equations

JO - Journal of the European Mathematical Society

PY - 2006

PB - European Mathematical Society Publishing House

VL - 008

IS - 2

SP - 253

EP - 268

AB - 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 $\varepsilon $ and the number of positive solutions increases to $\infty $ as $\varepsilon \rightarrow 0$. 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.

LA - eng

KW - nonlinear Schrödinger equations; singular perturbations; adiabatic profiles; nonlinear Schrödinger equations; singular perturbations; adiabatic profiles

UR - http://eudml.org/doc/277367

ER -

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