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

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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