Author:
A. M. A. El-Sayed ,F. Gaafar ,M. El-Gendy
Abstract
In this paper we are concerned with a problem of of a delay stochastic differential equation with nonlocal condition, the solution is represented as stochastic integral equation that contain mean square Riemann integral. We study the existence of at least mean square continuous solution for this problem. The existence of the maximal and minimal solutions will be proved.
Reference14 articles.
1. L. Arnold, Stochastic Differential Equations :theory and applications, A Wiley-Interscience Publication Copyright by J. Wiley and Sons, New York, (1974).
2. A. T. Bharucha-Teid, fixed point theorems in probabilistic analysis, Bulletin of the American Mathematical Society , 82(5) (1976).
3. A. Boucherif, A first-order differential inclusions with nonlocal initial conditions, Applied Mathematics Letters, 15 (2002), 409-414.
4. A. Boucherif and Radu Precup, On the nonlocal initial value problem for first order differential equations, Fixed Point Theory, 4(2) (2003), 205-212.
5. L.Byszewski and V.Lakshmikantham, Theorem about the existence and uniqueness of a solution of a nonlocal abstract Cauchy problem in a Banach space, Applicable analysis, 40 (1991), 11-19.