Existence and uniqueness of positive solutions of a system of nonlinear algebraic equations

In this paper we consider the nonlinear system (gamma _i(x_i)=sum _{j=1}^{m}g_{ij} (x_j)), ( 1le i le m). We give sufficient conditions which imply the existence and uniqueness of positive solutions of the system. Our theorem extends earlier results known in the literature. Several examples illustrate the main result.