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Existence, Uniqueness and Qualitative Properties of Global Solutions of Abstract Differential Equations with State-Dependent Delay

Part of: Miscellaneous topics - Partial differential equations Groups and semigroups of linear operators, their generalizations and applications Functional-differential and differential-difference equations

Published online by Cambridge University Press:  30 January 2019

Eduardo Hernández  and
Jianhong Wu
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 (lalohm@ffclrp.usp.br)
Jianhong Wu
Affiliation:
Department of Mathematics and Statistics, York University, Toronto, Ontario, M3J 1P3, Canada (wujh@mathstat.yorku.ca)
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Abstract

We study the existence, uniqueness and qualitative properties of global solutions of abstract differential equations with state-dependent delay. Results on the existence of almost periodic-type solutions (including, periodic, almost periodic, asymptotically almost periodic and almost automorphic solutions) are proved. Some examples of partial differential equations with state-dependent delay arising in population dynamics are presented.

Keywords

state-dependent delay equationsglobal solutionsstrict solutionsanalytic semigrouppartial differential equations

MSC classification

Primary: 34K30: Equations in abstract spaces
Secondary: 35R10: Partial functional-differential equations 47D06: One-parameter semigroups and linear evolution equations
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 62 , Issue 3 , August 2019 , pp. 771 - 788
Copyright
Copyright © Edinburgh Mathematical Society 2019 

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