Existence of Semi Linear Impulsive Neutral Evolution Inclusions with Infinite Delay in Frechet Spaces

Dimplekumar N. Chalishajar, Kulandhivel Karthikeyan and Annamalai Anguraj
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Dimplekumar N. Chalishajar: Department of Applied Mathematics, Virginia Military Institute (VMI), 431 Mallory Hall, Lexington, VA 24450, USA
Kulandhivel Karthikeyan: Department of Mathematics, KSR College of Technology, Tiruchengode 637215, India
Annamalai Anguraj: Department of Mathematics, PSG College of Arts and Science, Coimbatore 641014 , India

Mathematics, 2016, vol. 4, issue 2, 1-17

Abstract: In this paper, sufficient conditions are given to investigate the existence of mild solutions on a semi-infinite interval for first order semi linear impulsive neutral functional differential evolution inclusions with infinite delay using a recently developed nonlinear alternative for contractive multivalued maps in Frechet spaces due to Frigon combined with semigroup theory. The existence result has been proved without assumption of compactness of the semigroup. We introduced a new phase space for impulsive system with infinite delay and claim that the phase space considered by different authors are not correct.

Keywords: impulsive differential inclusions; fixed point; Frechet spaces; nonlinear alternative due to Frigon (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2016
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