The paper is devoted to nonlinear evolution equations with nonhomogenous boundary conditions of white noise type. Necessary and sufficient conditions for the existence of solutions in the linear case are given. It is also shown that if the nonlinearity satisfies appropriate dissipativity conditions the nonlinear equation has a solution as well. The results are applied to equations with polynomial nonlinearities Keywords: Stochastic evolution equationsnonhomogenous boundary conditionswhite-noisedissipativity
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Prato et al. (1993) studied this question.
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