This article presents the results on existence, uniqueness and stability of mild solutions to neutral stochastic functional evolution integro-differential equations with non-Lipschitz condition and Lipschitz condition. The existence of mild solutions for the equations are discussed by means of semigroup theory and theory of resolvent operator. Under some sufficient conditions, the results are obtained by using the method of successive approximation and Bihari’s inequality. Moreover, an example is given to illustrate our results.
C. .Parthasarathy, M. Arjunan, M., and Dr. Vinodkumar A., “Existence, Uniqueness and Stability of Neutral Stochastic Functional Integro-differential Evolution Equations with Infinite Delay”, International Journal of Computer Applications (0975 - 8887), vol. 65, pp. 1–7, 2013.