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Existence and multiplicity of periodic solutions to differential equations with attractive singularities

Part of: Boundary value problems Qualitative theory

Published online by Cambridge University Press:  12 April 2021

José Godoy ,
Robert Hakl Open the ORCID record for Robert Hakl [Opens in a new window]  and
Xingchen Yu
José Godoy
Affiliation:
Institute of Mathematics, Czech Academy of Sciences, Žižkova 22, 616 62 Brno, Czech Republic (godoy@math.cas.cz; hakl@ipm.cz)
Robert Hakl
Affiliation:
Institute of Mathematics, Czech Academy of Sciences, Žižkova 22, 616 62 Brno, Czech Republic (godoy@math.cas.cz; hakl@ipm.cz)
Xingchen Yu
Affiliation:
School of Mathematics and Statistics, Nanjing University of Information Science and Technology, Nanjing210044, P.R. China (yuxingchen0@yeah.net)
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Abstract

The existence and multiplicity of T-periodic solutions to a class of differential equations with attractive singularities at the origin are investigated in the paper. The approach is based on a new method of construction of strict upper and lower functions. The multiplicity results of Ambrosetti–Prodi type are established using a priori estimates and certain properties of topological degree.

Keywords

periodic solutionsupper and lower functionsmultiplicity results

MSC classification

Primary: 34C25: Periodic solutions
Secondary: 34B18: Positive solutions of nonlinear boundary value problems
Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 152 , Issue 2 , April 2022 , pp. 402 - 427
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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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