Abstract
In this paper, we study the existence and uniqueness of solutions of systems of semilinear PDE's by a probabilistic method based upon the nonlinear Feynman-Kac formula, introduced by E. Pardoux and S. Peng in [13]. Our contribution to this topic is to weaken the Lipschitz assumption on the coefficients of the linear part of the operator, assuming nevertheless the existence of a Lyapunov function to ensure the non-explosion of the associated diffusion process. This extension was motivated by problems arising in stochastic dynamical systems theory