On a new class of abstract impulsive differential equations

Hernández, Eduardo; O’Regan, Donal

doi:10.1090/S0002-9939-2012-11613-2

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ISSN 1088-6826(online) ISSN 0002-9939(print)

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
Posted: October 25, 2012
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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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