Title: Existence and stability solutions of second-order partial neutral stochastic nonlinear differential systems with infinite delay

Authors: Chinnasamy Parthasarathy

Addresses: Department of Mathematics, Sri Shakthi Institute of Engineering and Technology, Coimbatore 641062, Tamil Nadu, India

Abstract: In this paper we consider a class of second-order neutral stochastic differential equations with infinite delay. First we establish a new set of sufficient conditions for the existence and uniqueness results for the system of equations which are discussed under non-Lipschitz with Lipschitz condition by the means of the successive approximation and theory of cosine families. Moreover, we give the continuous dependence of solutions on the initial data by the way of corollary of the Bihari's inequality. Finally, an example is provided to illustrate our results.

Keywords: stochastic evolution equations; cosine family; successive approximation; Bihari's inequality; neutral stochastic differential equations; nonlinear differential systems; infinite delay.

DOI: 10.1504/IJDSDE.2015.071003

International Journal of Dynamical Systems and Differential Equations, 2015 Vol.5 No.3, pp.220 - 235

Received: 24 Jul 2014
Accepted: 21 Dec 2014
Published online: 05 Aug 2015 *

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