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${\mathcal{S}}$-ASYMPTOTICALLY PERIODIC SOLUTIONS FOR ABSTRACT EQUATIONS WITH STATE-DEPENDENT DELAY

Part of: Differential equations in abstract spaces Partial differential equations Qualitative theory Groups and semigroups of linear operators, their generalizations and applications

Published online by Cambridge University Press:  15 August 2018

EDUARDO HERNÁNDEZ Open the ORCID record for EDUARDO HERNÁNDEZ [Opens in a new window]  and
MICHELLE PIERRI Open the ORCID record for MICHELLE PIERRI [Opens in a new window]
EDUARDO HERNÁNDEZ*
Affiliation:
Departamento de Computação e Matemática, Faculdade de Filosofia Ciências e Letras de Ribeirão Preto, Universidade de São Paulo, CEP 14040-901 Ribeirão Preto, SP, Brazil email [email protected]
MICHELLE PIERRI
Affiliation:
Departamento de Computação e Matemática, Faculdade de Filosofia Ciências e Letras de Ribeirão Preto, Universidade de São Paulo, CEP 14040-901 Ribeirão Preto, SP, Brazil email [email protected]
*
✉[email protected]
Rights & Permissions [Opens in a new window]

Abstract

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We study the existence and uniqueness of ${\mathcal{S}}$-asymptotically periodic solutions for a general class of abstract differential equations with state-dependent delay. Some examples related to problems arising in population dynamics are presented.

Keywords

𝓢-asymptotically periodic functionsanalytic semigroupsstate-dependent delayabstract differential equationsexistence and uniqueness of solutions

MSC classification

Primary: 34G20: Nonlinear equations
Secondary: 34C27: Almost and pseudo-almost periodic solutions 35B40: Asymptotic behavior of solutions 47D06: One-parameter semigroups and linear evolution equations
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 98 , Issue 3 , December 2018 , pp. 456 - 464
Copyright
© 2018 Australian Mathematical Publishing Association Inc. 

Footnotes

The work of the first author was supported by São Paulo Research Foundation (FAPESP), grant number 2017/13145-8.

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