Geodesic
On the Number of Unbounded Solution Branches in a Neighborhood of an Asymptotic Bifurcation Point
Funkcionalʹnyj analiz i ego priloženiâ, Tome 39 (2005) no. 3, pp. 37-53

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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, asymptotically homogeneous operator, periodic oscillations, subharmonic.
Mots-clés : solution branch 
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     title = {On the {Number} of {Unbounded} {Solution} {Branches} in a {Neighborhood} of an {Asymptotic} {Bifurcation} {Point}},
     journal = {Funkcionalʹnyj analiz i ego prilo\v{z}eni\^a},
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A. M. Krasnosel'skii; D. I. Rachinskii. On the Number of Unbounded Solution Branches in a Neighborhood of an Asymptotic Bifurcation Point. Funkcionalʹnyj analiz i ego priloženiâ, Tome 39 (2005) no. 3, pp. 37-53. http://geodesic.mathdoc.fr/item/FAA_2005_39_3_a3/