The stochastic parabolic partial differential equation with non-Lipschitz coefficients on the unbounded domain

We consider the existence and uniqueness of the stochastic heat equation driven by the space-time white noise under the weaker conditions of the coefficients than the Lipschitz conditions. In order to show the existence of the solution, we investigate the sequence of the successive approximations under two kinds of conditions. (c) 2007 Elsevier Inc. All rights reserved.