RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB
General information
Latest issue
Archive
Impact factor
Subscription
License agreement
Submit a manuscript

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Funktsional. Anal. i Prilozhen.:
Year:
Volume:
Issue:
Page:
Find






Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register


Funktsional. Anal. i Prilozhen., 2005, Volume 39, Issue 3, Pages 37–53 (Mi faa73)  

This article is cited in 5 scientific papers (total in 5 papers)

On the Number of Unbounded Solution Branches in a Neighborhood of an Asymptotic Bifurcation Point

A. M. Krasnosel'skii, D. I. Rachinskii

Institute for Information Transmission Problems, Russian Academy of Sciences

Abstract: We suggest a method for studying asymptotically linear vector fields with a parameter. The method permits one to prove theorems on asymptotic bifurcation points (bifurcation points at infinity) for the case of double degeneration of the principal linear part. We single out a class of fields that have more than two unbounded branches of singular points in a neighborhood of a bifurcation point. Some applications of the general theorems to bifurcations of periodic solutions and subharmonics as well as to the two-point boundary value problem are given.

Keywords: asymptotic bifurcation point, solution branch, asymptotically homogeneous operator, periodic oscillations, subharmonic

DOI: https://doi.org/10.4213/faa73

Full text: PDF file (272 kB)
References: PDF file   HTML file

English version:
Functional Analysis and Its Applications, 2005, 39:3, 194–206

Bibliographic databases:

UDC: 517.988.67
Received: 15.09.2003

Citation: A. M. Krasnosel'skii, D. I. Rachinskii, “On the Number of Unbounded Solution Branches in a Neighborhood of an Asymptotic Bifurcation Point”, Funktsional. Anal. i Prilozhen., 39:3 (2005), 37–53; Funct. Anal. Appl., 39:3 (2005), 194–206

Citation in format AMSBIB
\Bibitem{KraRac05}
\by A.~M.~Krasnosel'skii, D.~I.~Rachinskii
\paper On the Number of Unbounded Solution Branches in a Neighborhood of an Asymptotic Bifurcation Point
\jour Funktsional. Anal. i Prilozhen.
\yr 2005
\vol 39
\issue 3
\pages 37--53
\mathnet{http://mi.mathnet.ru/faa73}
\crossref{https://doi.org/10.4213/faa73}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2174605}
\zmath{https://zbmath.org/?q=an:1128.47055}
\transl
\jour Funct. Anal. Appl.
\yr 2005
\vol 39
\issue 3
\pages 194--206
\crossref{https://doi.org/10.1007/s10688-005-0038-0}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000232583600004}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-26244458328}


Linking options:
  • http://mi.mathnet.ru/eng/faa73
  • https://doi.org/10.4213/faa73
  • http://mi.mathnet.ru/eng/faa/v39/i3/p37

    SHARE: VKontakte.ru FaceBook Twitter Mail.ru Livejournal Memori.ru


    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Ya. M. Dymarskii, “Manifold Method in Eigenvector Theory of Nonlinear Operators”, Journal of Mathematical Sciences, 154:5 (2008), 655–815  mathnet  crossref  mathscinet  zmath  elib
    2. Krasnosel'skii, AM, “On Disconnected Unbounded Sets of Forced Oscillations”, Doklady Mathematics, 78:2 (2008), 660  crossref  mathscinet  zmath  isi  scopus
    3. A. M. Krasnosel'skii, D. I. Rachinskii, “Criteria of resonance origin in a single-circuit control system with saturation”, Autom. Remote Control, 69:8 (2008), 1297–1310  mathnet  crossref  mathscinet  zmath  isi
    4. Krasnosel'skii, AM, “Double degeneracy in the problem on unbounded branches of forced oscillations”, Doklady Mathematics, 77:2 (2008), 170  crossref  mathscinet  zmath  isi  scopus
    5. Krasnosel'skii A.M., “Unbounded branches of periodic solutions”, Differ. Equ., 45:3 (2009), 344–364  crossref  mathscinet  zmath  isi  elib  scopus
  • Функциональный анализ и его приложения Functional Analysis and Its Applications
    Number of views:
    This page:320
    Full text:116
    References:61
    First page:1

     
    Contact us:
     Terms of Use  Registration  Logotypes © Steklov Mathematical Institute RAS, 2020