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

Using inverse positivity properties and Brouwerʹs fixed point theorem, we derive existence and uniqueness results for certain nonlinear systems of equations with off diagonal nonlinearity. Systems of the type considered arise, e.g., from stable finite volume discretizations of viscous nonlinear conservation laws. Though connected to such an important field of applications, results of this type are seldom used.