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Funktsional'nyi Analiz i ego Prilozheniya, 2005, Volume 39, Issue 3, Pages 37–53
DOI: https://doi.org/10.4213/faa73 (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
Full-text PDF (272 kB) Citations (5)
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DOI: https://doi.org/10.4213/faa73
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.
Received: 15.09.2003
English version:
Functional Analysis and Its Applications, 2005, Volume 39, Issue 3, Pages 194–206
DOI: https://doi.org/10.1007/s10688-005-0038-0
Bibliographic databases:
Document Type: Article
UDC: 517.988.67
Language: Russian
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
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    • This publication is cited in the following 5 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Функциональный анализ и его приложения Functional Analysis and Its Applications
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