An New Existence Theorem for Systems of Nonlinear Equations

As a generalization of the intermediate value theorem in Rn,G.Aumann got an existence theorem of solution for systems of nonlinear equations defined on a n dimensional rectangle.By using Brouwer fixed point theorem,J.Rohn generalized the theorem under the hypothesis that the domain is a compact convex set.In this paper,using Brouwer topological degree theory,it is proved that the theorem still holds if we substitute star shape region for convex set.