In this paper, the existence and exponential stability of mild solutions of semilinear differential equations with random impulses are studied under non-uniqueness in a real separable Hilbert space. The results are obtained by using the Leray–Schauder alternative fixed point theorem.
A. Anguraj, Wu, S., and Dr. Vinodkumar A., “The existence and exponential stability of semilinear functional differential equations with random impulses under non-uniqueness”, Nonlinear Analysis: Theory, Methods & Applications, vol. 74, pp. 331 - 342, 2011.