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Mediterranean Journal of Mathematics

, Volume 13, Issue 4, pp 1685–1708 | Cite as

Global Solutions for Abstract Differential Equations with Non-Instantaneous Impulses

  • Michelle PierriEmail author
  • Hernán R. Henríquez
  • Andréa Prokopczyk
Article

Abstract

In this note we study the existence of global solutions for a class of impulsive abstract differential equations with non-instantaneous impulses. Specifically, we establish the existence of mild solutions on \({[0, \infty)}\) and the existence of \({\mathcal{S}}\)-asymptotically \({\omega}\)-periodic mild solutions. Our results are based on the Hausdorff measure of non-compactness. Some applications involving partial differential equations are considered.

Keywords

First-order abstract Cauchy problem impulsivedifferential equations mild solutions asymptotically periodic solutions strongly continuous semigroups of linear operators 

Mathematics Subject Classification

34K30 34K45 35R12 47D06 

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Copyright information

© Springer Basel 2015

Authors and Affiliations

  • Michelle Pierri
    • 1
    Email author
  • Hernán R. Henríquez
    • 2
  • Andréa Prokopczyk
    • 3
  1. 1.Departamento de Computação e MatemáticaFaculdade deFilosofia, Ciências e Letras de Ribeirão Preto. Universidade de São PauloRibeirão PretoBrazil
  2. 2.Departamento de MatemáticaUniversidad de Santiago USACHSantiagoChile
  3. 3.Instituto de Biociências, Letras e Ciências ExatasUniversidade Estadual PaulistaSão José do Rio PretoBrazil

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