Stationary solutions of semilinear Schrödinger equations with trapping potentials in supercritical dimensions

Filip Ficek

Archivum Mathematicum (2023)

  • Issue: 1, page 31-38
  • ISSN: 0044-8753

Abstract

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Nonlinear Schrödinger equations are usually investigated with the use of the variational methods that are limited to energy-subcritical dimensions. Here we present the approach based on the shooting method that can give the proof of existence of the ground states in critical and supercritical cases. We formulate the assumptions on the system that are sufficient for this method to work. As examples, we consider Schrödinger-Newton and Gross-Pitaevskii equations with harmonic potentials.

How to cite

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Ficek, Filip. "Stationary solutions of semilinear Schrödinger equations with trapping potentials in supercritical dimensions." Archivum Mathematicum (2023): 31-38. <http://eudml.org/doc/298983>.

@article{Ficek2023,
abstract = {Nonlinear Schrödinger equations are usually investigated with the use of the variational methods that are limited to energy-subcritical dimensions. Here we present the approach based on the shooting method that can give the proof of existence of the ground states in critical and supercritical cases. We formulate the assumptions on the system that are sufficient for this method to work. As examples, we consider Schrödinger-Newton and Gross-Pitaevskii equations with harmonic potentials.},
author = {Ficek, Filip},
journal = {Archivum Mathematicum},
keywords = {nonlinear Schrödinger equation; stationary solutions; supercritical dimensions; shooting method},
language = {eng},
number = {1},
pages = {31-38},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {Stationary solutions of semilinear Schrödinger equations with trapping potentials in supercritical dimensions},
url = {http://eudml.org/doc/298983},
year = {2023},
}

TY - JOUR
AU - Ficek, Filip
TI - Stationary solutions of semilinear Schrödinger equations with trapping potentials in supercritical dimensions
JO - Archivum Mathematicum
PY - 2023
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
IS - 1
SP - 31
EP - 38
AB - Nonlinear Schrödinger equations are usually investigated with the use of the variational methods that are limited to energy-subcritical dimensions. Here we present the approach based on the shooting method that can give the proof of existence of the ground states in critical and supercritical cases. We formulate the assumptions on the system that are sufficient for this method to work. As examples, we consider Schrödinger-Newton and Gross-Pitaevskii equations with harmonic potentials.
LA - eng
KW - nonlinear Schrödinger equation; stationary solutions; supercritical dimensions; shooting method
UR - http://eudml.org/doc/298983
ER -

References

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