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Local and global existence and uniqueness of solution for abstract differential equations with state-dependent argument

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

Published online by Cambridge University Press:  26 April 2023

Eduardo Hernandez Open the ORCID record for Eduardo Hernandez [Opens in a new window] ,
Denis Fernandes  and
Akbar Zada
Eduardo Hernandez
Affiliation:
Departamento de Computaçãoe Matemática, Faculdade de Filosofia, Ciências e Letras de Ribeirão Preto, Universidade de São Paulo, CEP 14040-901, Ribeirão Preto, Sao Paulo, Brazil (lalohm@ffclrp.usp.br)
Denis Fernandes
Affiliation:
Department of Mathematics and Statistics, York University, Toronto, ON M3J 1P3, Canada (denisf@yorku.ca)
Akbar Zada
Affiliation:
Department of Mathematics, University of Peshawar, Peshawar 25000, Pakistan (akbarzada@uop.edu.pk)
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Abstract

We study the local and global existence and uniqueness of mild solution for a general class of abstract differential equations with state-dependent argument. In the last section, some examples on partial differential equations with state-dependent argument are presented.

Keywords

state-dependent argumentlocal solutionglobal solutionuniqueness of solutionmild solutionclassical solutionstrict solution

MSC classification

Primary: 34K30: Equations in abstract spaces 47D06: One-parameter semigroups and linear evolution equations
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 66 , Issue 2 , May 2023 , pp. 305 - 345
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Copyright
© The Author(s), 2023. Published by Cambridge University Press on Behalf of The Edinburgh Mathematical Society.

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