New results for Brillouin electron beam focusing system
type: Item
instance of: scholarly article
title: New results for Brillouin electron beam focusing system
zbMATH Open document ID: 1385.34023
author: Zhibo Cheng
author: Shao-Wen Yao
published in: Boundary Value Problems
publication date: 2017-11-14T00:00:00Z
review text: In this paper, the authors study the following singular equation \[ x''(t)+a(t)x(t)=\frac{1}{x(t)}, \] where \(a(t)\in C(\mathbb{R}, [0,+\infty))\) and \(a(t+T)=a(t)\;\forall t\in \mathbb{R}\). Under the assumption \[ |a|_\infty:=\max_{t\in[0,T]}|a(t)|<\frac{4\pi^2}{T^2} \] the existence of positive \(T\)-periodic solutions is proved. The proof is based on the Manasevich-Mawhin's theorem. As an application, they obtain the existence of positive \(2\pi\)-periodic solutions for the Brillouin electron beam focusing equation \[ x''+a(1+\cos 2t)x=\frac{1}{x}, \] where \(a\in(0,\frac{1}{2})\).
reviewed by: Chun Li
Mathematics Subject Classification ID: 34B18
Mathematics Subject Classification ID: 34C25
Mathematics Subject Classification ID: 34B16
Mathematics Subject Classification ID: 47N20
zbMATH DE Number: 6806918
zbMATH Keywords: Brillouin electron beam focusing system
zbMATH Keywords: positive periodic solution
zbMATH Keywords: singular
Wikidata QID: Q59525623
MaRDI profile type: Publication
full work available at URL: s13661-017-0800-2
OpenAlex ID: W2615427410
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cites work: Q4516849
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DOI: 10.1186/S13661-017-0800-2
description: scientific article; zbMATH DE number 6806918