This article is cited 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.

UDC: 517.988.67

Received: 15.09.2003

DOI: 10.4213/faa73

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

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