Discontinuity, Nonlinearity, and Complexity
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) 112  DOI:10.5890/DNC.2019.03.001
A. Anguraj, K. Banupriya
Department of Mathematics, PSG College of Arts and Science, Coimbatore641 014, Tamil Nadu, India
Department of Mathematics with CA, PSG College of Arts and Science, Coimbatore641 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 nonLipschitz 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 MRP5820/15(SERO/UGC)) for supporting the present work.
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