On The Existence of A Unique Solution for Systems of Ordinary Differential Equations of First Order

Abdussalam A. Bojeldain, Saif Alislam E. Muhammed

In this paper, we state and prove a theorem for local existence of a unique solution for a system of nonlinear ordinary differential equations ( NODE ) of first order by proving that the nonlinear operator of this system is contractive in a metric space subset of the Banach space consisting of the bounded differentiable functions on the real numbers and equipped with a Bielescki's type norm.  Finally, we give examples to illustrate our result.