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Discontinuity, Nonlinearity, and Complexity

Dimitry Volchenkov (editor), Dumitru Baleanu (editor)

Dimitry Volchenkov(editor)

Mathematics & Statistics, Texas Tech University, 1108 Memorial Circle, Lubbock, TX 79409, USA

Email: dr.volchenkov@gmail.com

Dumitru Baleanu (editor)

Cankaya University, Ankara, Turkey; Institute of Space Sciences, Magurele-Bucharest, Romania

Email: dumitru.baleanu@gmail.com


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

Discontinuity, Nonlinearity, and Complexity 6(1) (2017) 19--34 | DOI:10.5890/DNC.2017.03.003

Dimplekumar N. Chalishajar; K. Karthikeyan; A. Anguraj

Department of Applied Mathematics, Virginia Military Institute (VMI), 431, Mallory Hall, Lexington, VA 24450, USA

Department of Mathematics, KSR College of Technology, Tiruchengode, Tamil Nadu 637215, India

Department of Mathematics, PSG College of Arts and Science, Coimbatore, Tamil Nadu 641 014, India

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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 contractivemultivalued 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 study a new phase space for impulsive system with infinite delay.

Acknowledgments

Authors wish to express their gratitude to the anonymous referees for their valuable suggestions and comments for improving this manuscript.

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