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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.
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
Linking options:
https://www.mathnet.ru/eng/faa73https://doi.org/10.4213/faa73 https://www.mathnet.ru/eng/faa/v39/i3/p37
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Abstract page: | 516 | Full-text PDF : | 224 | References: | 92 | First page: | 1 |
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