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On a new class of abstract impulsive differential equations


Authors: Eduardo Hernández and Donal O’Regan
Journal: Proc. Amer. Math. Soc. 141 (2013), 1641-1649
MSC (2010): Primary 34K30, 34K45, 35R12, 47D06
DOI: https://doi.org/10.1090/S0002-9939-2012-11613-2
Published electronically: October 25, 2012
MathSciNet review: 3020851
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Abstract | References | Similar Articles | Additional Information

Abstract: In this note we introduce a new class of abstract impulsive differential equations for which the impulses are not instantaneous. We introduce the concepts of mild and classical solution and we establish some results on the existence of these types of solutions. An example involving a partial differential equation is presented.


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Additional Information

Eduardo Hernández
Affiliation: Departamento de Computação e Matemática, Faculdade de Filosofia, Ciencias e Letras de Ribeirão Preto, Universidade de São Paulo, CEP 14040-901 Ribeirão Preto, SP, Brazil
Email: lalohm@ffclrp.usp.br

Donal O’Regan
Affiliation: School of Mathematics, Statistics and Applied Mathematics, National University of Ireland, Galway, Ireland
Email: donal.oregan@nuigalway.ie

DOI: https://doi.org/10.1090/S0002-9939-2012-11613-2
Keywords: Impulsive differential equation, mild solution, classical solution, $C_{0}$-semigroup of linear operators.
Received by editor(s): September 2, 2011
Published electronically: October 25, 2012
Communicated by: Yingfei Yi
Article copyright: © Copyright 2012 American Mathematical Society

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