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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, Uniqueness and Stability Results for Impulsive Neutral Stochastic Functional Differential Equations with Infinite Delay and Poisson Jumps

Discontinuity, Nonlinearity, and Complexity 8(1) (2019) 1--12 | DOI:10.5890/DNC.2019.03.001

A. Anguraj, K. Banupriya

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

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

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Abstract

In this paper, we study the existence and uniqueness of mild solutions of impulsive neutral stochastic functional differential equations with infinite delay and Poisson jumps under non-Lipschitz conditionwith Lipschitz condition being considered as a special case by means of the successive approximation. Further, We study the continuous dependence of solutions on the initial value by means of a corollary of the Bihari inequality.

Acknowledgments

The authors would like to express sincere gratitude to the reviewers for his/her valuable suggestions. The second author wishes to acknowledge the UGC,India (F MRP-5820/15(SERO/UGC)) for supporting the present work.

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