Acta Mathematica Hungarica
Volume/Issue:
Volume 108: Issue 3
Fixed points, Volterra equations, and Becker’s resolvent
Author:
T. A. Burton Northwest Research Institute 732 Caroline St., Port Angeles, WA 98362, U.S.A.

Search for other papers by T. A. Burton in
Current site
Google Scholar
PubMed Close
Pages:
261–281
Online Publication Date:
19 Jul 2005
Publication Date:
01 Aug 2005
Article Category:
Research Article
DOI:
https://doi.org/10.1007/s10474-005-0224-9
Keywords:
stability; fixed points; Volterra equations; resolvent; Liénard equation; relaxation oscillations
Restricted access

Summary In a recent paper we derived a stability criterion for a Volterra equation which is based on the contraction mapping principle. It turns out that this criterion has significantly wider application. In particular, when we use Becker’s form of the resolvent it readily establishes critical resolvent properties which have been very illusive when investigated by other techniques. First, it enables us to show that the resolvent is L1. Next, it allows us to show that the resolvent satisfies a uniform bound and that it tends to zero. These properties are then used to prove boundedness of solutions of a nonlinear problem, establish the existence of periodic solutions of a linear problem, and to investigate asymptotic stability properties. We also apply the results to a Liénard equation with distributed delay and possibly negative damping so that relaxation oscillations may occur.

  • Collapse
  • Expand
Cover Acta Mathematica Hungarica
Acta Mathematica Hungarica
Print ISSN:
0236-5294
Online ISSN:
1588-2632

To see the editorial board, please visit the website of Springer Nature.

Manuscript Submission: HERE

For subscription options, please visit the website of Springer Nature.

Acta Mathematica Hungarica
Language English
Size B5
Year of
Foundation		 1950
Volumes
per Year		 3
Issues
per Year		 6
Founder Magyar Tudományos Akadémia  
Founder's
Address		 H-1051 Budapest, Hungary, Széchenyi István tér 9.
Publisher Akadémiai Kiadó
Springer Nature Switzerland AG
Publisher's
Address		 H-1117 Budapest, Hungary 1516 Budapest, PO Box 245.
CH-6330 Cham, Switzerland Gewerbestrasse 11.
Responsible
Publisher		 Chief Executive Officer, Akadémiai Kiadó
ISSN 0236-5294 (Print)
ISSN 1588-2632 (Online)

Monthly Content Usage

Abstract Views Full Text Views PDF Downloads
Mar 2024 0 0 0
Apr 2024 5 0 0
May 2024 2 0 0
Jun 2024 6 0 0
Jul 2024 3 0 0
Aug 2024 13 0 0
Sep 2024 1 0 0