TABLE OF CONTENTS In previous sections we considered a single nonlinear ODE. However, the same conclusions also hold for a system of first-order ODEs
with ICs
which may be written compactly as
The result, obtained by following the same steps as before, can be summarized as follows (cf. Ince, 1956, section 3.3; Brauer and Nohel, 1989, section 3.4).
Let the functions f i, i = 1,2, , n, be single-valued and continuous in their ( n + 1) arguments in the domain 
defined by
and let
in this domain. Also, define
and if h < a, restrict x to x ? x 0 ? h. Furthermore, let the functions f i satisfy the Lipschitz condition in 
:
Then there exist unique, continuous functions of x, y i( x) satisfying eqs. (2.7.1) and (2.7.2). These functions are obtained from the sequences
in the limit as j ? ?, and they are continuous with respect to the initial conditions y 0 or parameters in f. These solutions can be extended in both directions of x 0 until y( x) remains finite or until its graph meets the boundary of 
, where y denotes the norm of y, defined by eq. (1.5.4).
This result is not only valuable by itself, but it can also be employed for...
