الفهرس 
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Abstract
t > 0
Theory of differential equation is one of the most important and useful branch of mathe-
matical analysis. In this thesis we study some coupled systems of non linear differential
equations.
The thesis is organized in three chapters as follows:
In Chapter 1
we collect together some preliminaries, notations and known results which will be used in
the for coming chapters.
Chapter 2
Consists of two parts , the first part deals with the existence of a unique continuous solution
for the coupled system of the functional differential equations .
dx
dt= fl(t, Y(<P2(t)), x (0) = Xo
dy
dt = het, X(<Pl(t)), Y (0) = Yo
t > 0
under the assumption that the functions fi satisfy Lipschitz condition,i = 1,2 .
Also.the uniform stability of this solution will be studied.
The second part deals with the existence of at least one continuous solution for the coupled
system of differential equation
dx
dt = het, yet)), x (0)
Xo
t > 0
dy
dt= het, x(t)), y (0) = Yo
t > 0
and the coupled system of the functional differential equations.
dx
dt = het, y(</J2(t)), x (0) = Xo
t > 0
dy
dt
het, X(<Pl(t)), y (0)
Yo
t > 0
In Chapter 3,
We study the existence of a unique continuous solution for the coupled system of difleren-
ti”al equations.
dx
dt
dy
het, dt)’x (0) = Xo
t > 0
dy dx
dt= h(t, dt)’ y (0) = Yo
and the coupled system of differential equations .
t > 0
dx
dt
dy
het, yet), dt)’ x (0)
Xo
t > 0
dy dx
dt = het, x(t), dt)’y (0) = Yo
t > 0
under the assumption that the function h satisfy Lipschitz condition,i = 1,2 .
Also, the uniform stability of these solutions will be studied.