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Bifurcation at infinity for equations in spaces of vector-valued functions

Part of: Nonlinear operators and their properties

Published online by Cambridge University Press:  09 April 2009

P. Diamond ,
P. E. Kloeden ,
A. M. Krasnosel'skii  and
A. V. Pokrovskii
P. Diamond
Affiliation:
Department of Mathematics University of QueenslandBrisbane 4072Australia e-mail: pmd@maths.uq.oz.au
P. E. Kloeden
Affiliation:
CADSEM Deakin University Geelong3217Australia e-mail: kloeden@deakin.edu.au
A. M. Krasnosel'skii
Affiliation:
Institute for Information Transmission Problems19 Bolshoi Karetny lane Moscow 101447Russia e-mail: amk@ippi.ac.msk.su
A. V. Pokrovskii
Affiliation:
CADSEM Deakin UniversityGeelong 3217Australia e-mail: alexei@deakin.edu.au
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Abstract

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New existence conditions, under which an index at infinity can be calculated, are given for bifurcations at infinity of asymptotically linear equations in spaces of vector-valued functions. The case where a bounded nonlinearity has discontinuous principal homogeneous part is considered. The results are applied to 2π-periodic problems for two-dimensional systems of ordinary differential equations and to a vector two-point boundary value problem.

MSC classification

Secondary: 47H11: Degree theory 47H30: Particular nonlinear operators (superposition, Hammerstein, Nemytskiĭ, Uryson, etc.)
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 63 , Issue 2 , October 1997 , pp. 263 - 280
Copyright
Copyright © Australian Mathematical Society 1997

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