The existence and asymptotic behaviour of solutions to non-Lipschitz stochastic functional evolution equations driven by Poisson jumps

In this paper, we consider the existence and uniqueness of the energy solutions to the following non-Lipschitz stochastic functional evolution equation driven both by Brownian motion and by Poisson jumps where is a linear or nonlinear bounded operator, , and are measurable functions. We also investigate the almost sure exponential stability of energy solutions by using the energy equality for this equation.

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