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Standing waves of modified Schrödinger equations coupled with the Chern–Simons gauge theory

Part of: Equations of mathematical physics and other areas of application Elliptic equations and systems

Published online by Cambridge University Press:  12 March 2019

Pietro d'Avenia ,
Alessio Pomponio  and
Tatsuya Watanabe
Pietro d'Avenia
Affiliation:
Dipartimento di Meccanica, Matematica e Management Politecnico di Bari Via Orabona 4, 70125Bari, Italy (pietro.davenia@poliba.it; alessio.pomponio@poliba.it)
Alessio Pomponio
Affiliation:
Dipartimento di Meccanica, Matematica e Management Politecnico di Bari Via Orabona 4, 70125Bari, Italy (pietro.davenia@poliba.it; alessio.pomponio@poliba.it)
Tatsuya Watanabe
Affiliation:
Department of Mathematics, Faculty of Science, Kyoto Sangyo University, Motoyama, Kamigamo, Kita-ku, Kyoto-City603-8555, Japan (tatsuw@cc.kyoto-su.ac.jp)
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Abstract

We are interested in standing waves of a modified Schrödinger equation coupled with the Chern–Simons gauge theory. By applying a constraint minimization of Nehari-Pohozaev type, we prove the existence of radial ground state solutions. We also investigate the nonexistence for nontrivial solutions.

Keywords

ground state solutiongauged Schrödinger equationvariational method

MSC classification

Primary: 35J62: Quasilinear elliptic equations
Secondary: 35J20: Variational methods for second-order elliptic equations 35Q60: PDEs in connection with optics and electromagnetic theory
Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 150 , Issue 4 , August 2020 , pp. 1915 - 1936
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Copyright
Copyright © Royal Society of Edinburgh 2019

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