In the present paper we deal with stochastic semilinear partial differential equations \(Lu= \gamma (u) + \sigma (u)\dot{\Xi }\) of parabolic type with (t, x)-depending coefficients which may admit a polynomial growth with respect to the space variable. Under suitable assumptions on the coefficients of the parabolic operator L, on the initial data and on the stochastic noise \(\Xi \) (more precisely, on the spectral measure \(\mathfrak M\) associated with \(\Xi \) ) we prove existence of a unique (mild) function-valued solution for the associated Cauchy problem.
