Stability of well-posed stochastic evolution equation

Abstract

The stability of a non-classical stochastic evolution equation with impulsive and nonlocal initial conditions is examined from a general perspective. We investigate the effect of the nonlocal conditions on the well-posedness and the stability of the solution. We show that the concept of Ulam-type stability holds for this class of equation under the given condition (1−MLηξ)<1. An example is also provided to support our claim.