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Conley index for manifold-valued retarded functional differential equations without uniqueness of solutions

Part of: Topological dynamics Functional-differential and differential-difference equations

Published online by Cambridge University Press:  19 April 2021

M. C. Carbinatto  and
K. P. Rybakowski
M. C. Carbinatto
Affiliation:
Departamento de Matemática, ICMC-USP, Caixa Postal 668, 13.560-970, São Carlos SP, Brazil (mdccarbi@icmc.usp.br)
K. P. Rybakowski
Affiliation:
Universität Rostock, Institut für Mathematik, Ulmenstraße 69, Haus 3, 18057, Rostock, Germany (krzysztof.rybakowski@uni-rostock.de)
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Abstract

We develop a Conley index theory for retarded functional differential equations $\dot x=f(x_{t})$ with values in a differentiable manifold and (merely) continuous nonlinearities f. We use this index to establish an existence result for nonconstant full solutions of such equations.

Keywords

infinite-dimensional dynamical systemsConley indexfunctional differential equations on manifolds

MSC classification

Primary: 37B30: Index theory, Morse-Conley indices
Secondary: 34K05: General theory

Information

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 152 , Issue 2 , April 2022 , pp. 428 - 449
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Copyright
Copyright © The Author(s), 2021. Published by Cambridge University Press on behalf of The Royal Society of Edinburgh

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