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.

We prove the existence of mild solutions for a partial neutral functional integrodifferential equation with unbounded delay using the Leray-Schauder alternative.  2004 Elsevier Inc. All rights reserved.

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