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

Published online by Cambridge University Press:  19 April 2021

M. C. Carbinatto
Affiliation:
Departamento de Matemática, ICMC-USP, Caixa Postal 668, 13.560-970, São CarlosSP, 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)

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.

Type
Research Article
Copyright
Copyright © The Author(s), 2021. Published by Cambridge University Press on behalf of The Royal Society of Edinburgh

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