Abstract.In this paper, we consider neutral stochastic functional differential equations with unbounded delay in a Hilbert space. Existence and uniqueness of solutions of such equations are established using local Lipschitz conditions on the nonlinear terms exploiting the contraction mapping principle. An example is given to illustrate the theory.

Received: November 26, 2008

AMS Subject Classification: 60H10

Key Words and Phrases: neutral stochastic functional differential equations, local Lipschitz conditions, existence and uniqueness of a solution, contraction mapping principle

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2009
Volume: 50
Issue: 1