Stochastic reaction-diffusion systems with multiplicative noise and non-Lipschitz reaction term

 We study existence and uniqueness of a mild solution in the space of continuous functions and existence of an invariant measure for a class of reaction-diffusion systems on bounded domains of ℝ ^d , perturbed by a multiplicative noise. The reaction term is assumed to have polynomial growth and to be locally Lipschitz-continuous and monotone. The noise is white in space and time if d=1 and coloured in space if d>1; in any case the covariance operator is never assumed to be Hilbert-Schmidt. The multiplication term in front of the noise is assumed to be Lipschitz-continuous and no restrictions are given either on its linear growth or on its degenaracy. Our results apply, in particular, to systems of stochastic Ginzburg-Landau equations with multiplicative noise. Received: 1 November 2001 / Revised version: 17 June 2002 / Published online: 14 November Mathematics Subject Classification (2000): 60H15, 35R60, 47A35