We consider semilinear evolution equations with some locally Lipschitz nonlinearities, perturbed by Banach space valued, continuous, and adapted stochastic process. We show that under some assumptions there exists a solution to the equation. Using the result we show that there exists a mild, continuous, global solution to a semilinear Itô equation with locally Lipschitz nonlinearites. An example of the equation is given.

Keywords:

evolution equation, mild solution, non-Lipschitz drift, Ito integral evolution equation, mild solution, non-Lipschitz drift, Ito integral

MSC Classifications:

60H20 show english descriptions Stochastic integral equations 60H20 - Stochastic integral equations

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