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

Felmer, 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 -