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Concentration phenomena for fractional magnetic NLS equations

Part of: Variational problems in infinite-dimensional spaces Partial differential equations Miscellaneous topics - Partial differential equations

Published online by Cambridge University Press:  28 May 2021

Vincenzo Ambrosio Open the ORCID record for Vincenzo Ambrosio [Opens in a new window]
Vincenzo Ambrosio*
Affiliation:
Dipartimento di Ingegneria Industriale e Scienze Matematiche, Università Politecnica delle Marche, Via Brecce Bianche, 12, 60131, Ancona, Italy ([email protected])
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Abstract

We study the multiplicity and concentration of complex-valued solutions for a fractional magnetic Schrödinger equation involving a scalar continuous electric potential satisfying a local condition and a continuous nonlinearity with subcritical growth. The main results are obtained by applying a penalization technique, generalized Nehari manifold method and Ljusternik–Schnirelman theory. We also prove a Kato's inequality for the fractional magnetic Laplacian which we believe to be useful in the study of other fractional magnetic problems.

Keywords

Fractional magnetic operatorsLjusternik–Schnirelman theoryvariational methods

MSC classification

Primary: 35A15: Variational methods
Secondary: 35R11: Fractional partial differential equations 35S05: Pseudodifferential operators 58E05: Abstract critical point theory (Morse theory, Ljusternik-Schnirelman (Lyusternik-Shnirel'man) theory, etc.)
Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 152 , Issue 2 , April 2022 , pp. 479 - 517
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Copyright
Copyright © The Author(s), 2021. Published by Cambridge University Press on behalf of The Royal Society of Edinburgh

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