Existence and uniqueness of solutions of certain systems of algebraic equations with off-diagonal nonlinearity

Using inverse positivity properties and Brouwer's fixed point theorem, we d erive existence and uniqueness results for certain nonlinear systems of equ ations with off diagonal nonlinearity. Systems of the type considered arise , e.g., from stable finite volume discretizations of viscous nonlinear cons ervation laws. Though connected to such an important field of applications, results of this type are seldom used. (C) 2001 IMACS. Published by Elsevie r Science B.V. All rights reserved.