An infinite sequence of localized semiclassical bound states for nonlinear Dirac equations
type: Item
instance of: scholarly article
title: An infinite sequence of localized semiclassical bound states for nonlinear Dirac equations
zbMATH Open document ID: 1403.35258
author: Xianqiang Yang
published in: Calculus of Variations and Partial Differential Equations
publication date: 2018-05-25T00:00:00Z
review text: The authors address a stationary three-dimensional Dirac equation which contains an external-potential term with a local energy minimum. The equation is either a linear one, or with nonlinearity \(\sim |u|u\). In the semi-classical limit, which corresponds to a small coefficient in front of the first-derivative terms in the Dirac equation, they provide a rigorous proof of the existence of an infinite number of bound states in a vicinity of the energy minimum (in previous works, the proof was produced only for the existence of the ground state, or a of a finite number of bound states, in a similar setting). The analysis is related to that addressing bound states in the Schrödinger equation, also in the semi-classical limit, and makes use of a variational approach.
reviewed by: B. A. Malomed
Mathematics Subject Classification ID: 35Q41
Mathematics Subject Classification ID: 35Q40
Mathematics Subject Classification ID: 49J35
Mathematics Subject Classification ID: 35A15
zbMATH DE Number: 6873452
zbMATH Keywords: Schrödinger equations
zbMATH Keywords: ground state
zbMATH Keywords: minimax principle
zbMATH Keywords: variational methods
MaRDI profile type: Publication
full work available at URL: s00526-018-1319-9
OpenAlex ID: W2793313102
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DOI: 10.1007/S00526-018-1319-9
description: scientific article; zbMATH DE number 6873452