Verification methods for nonlinear equations with saddle point functions (Q1410829)

A verification method for a system of nonlinear equations with saddle point functions is based on the equivalent reformulation of this system, under suitable assumptions, as a fixed point problem and then to use a certain fixed point theorem in order to obtain the existence of a fixed point. Using the Brouwer fixed point theorem, Theorem 3.1 in the paper provides an existence (and uniqueness) theorem, while Theorem 4.1 gives an existence result. A stationary Navier-Stokes equation is then used to illustrate Theorems 3.1 and 4.1 and to compare the results to other verification methods.