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Mathematics 2016, 4(2), 23; doi:10.3390/math4020023

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

1
Department of Applied Mathematics, Virginia Military Institute (VMI), 431 Mallory Hall, Lexington, VA 24450, USA
2
Department of Mathematics, KSR College of Technology, Tiruchengode 637215, India
3
Department of Mathematics, PSG College of Arts and Science, Coimbatore 641014 , India
These authors contributed equally to this work.
*
Author to whom correspondence should be addressed.
Academic Editor: Hari M. Srivastava
Received: 25 January 2016 / Revised: 21 March 2016 / Accepted: 25 March 2016 / Published: 6 April 2016
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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. View Full-Text
Keywords: impulsive differential inclusions; fixed point; Frechet spaces; nonlinear alternative due to Frigon impulsive differential inclusions; fixed point; Frechet spaces; nonlinear alternative due to Frigon
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

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Chalishajar, D.N.; Karthikeyan, K.; Anguraj, A. Existence of Semi Linear Impulsive Neutral Evolution Inclusions with Infinite Delay in Frechet Spaces. Mathematics 2016, 4, 23.

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