الفهرس 
Preliminary ConsiderationsOnly 14 pages are availabe for public view
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Abstract
This thesis aims to investigate the stability, boundedness, existence and uniqueness of solutions for some scalar higher-order nonlinear delay difierential equations.
In this thesis, we present some known results and derive new ones on the
stability and boundedness of solutions for nonlinear delay difierential equations.
Furthermore, we investigate the existence and uniqueness of periodic solutions for
a third-order neutral functional difierential equation with constant parameters.
This thesis is divided into four main chapters as the following:
In Chapter 1, we present some concepts and methods of the qualitative theory
of delay difierential equations, which are needed for the study of stability and
boundedness of the solutions for delay difierential equations.
Also, we introduce some theorems concerning the existence of periodic solutions for neutral functional difierential equations with constant parameters.
In Chapter 2, by constructing Lyapunov functionals, we establish new results
on the asymptotic stability and boundedness of solutions for a third-order neutral
delay difierential equation in the form
[h(x(t))x00(t)]0+[p(x(t))x0(t)]0 + g(x0(t ¡ r(t))) + f(x(t ¡ r(t)))
= e(t; x(t); x0(t); x00(t));
where h; p; g; f and e are continuous functions with g(0) = f(0) = 0; and the
derivatives h0(u) = dh du; p0(u) = du dp, exist and continuous.
If we put h(x(t)) = 1 and p(x(t)) = a in the previous equation, we get a special
iiicase that are considered in [55].
Numerical examples have been given to illustrate the main results.
In Chapter 3, with the aid of a suitable Lyapunov functional, we establish
a criteria to the case p = 0; the stability of the zero solution and the boundedness of all solutions in case p 6= 0; of third-order non-autonomous multiple delay
difierential equation of the form
...
x +a(t)f( _ x)˜ x + b(t)
nXi
=1
gi(x(t ¡ ri(t)); x_ (t ¡ ri(t))) + c(t)
nXi
=1
hi(x(t ¡ ri(t)))
= p(t; x; x; _ x; x ˜ (t ¡ r(t)));
where a(t); b(t) and c(t) are positive and continuous difierentiable functions on
[0; 1); f; gi and hi are continuous functions for all values of respective arguments,
with hi(0) = gi(x; 0) = 0:
The results of this chapter generalize those obtained in [42] where p = 0, by considering the previous equation is a difierential equation with a deviating argument,
where f( _ x) = 1 and g(x(t ¡ r(t)); x_ (t ¡ r(t))) = g(x(t ¡ r(t))):
We constructed two examples to illustrate our main results of stability and
boundedness.
Finally; in Chapter 4, by using Mawhin’s continuation theorem of coincidence
degree theory and analysis techniques, we investigate su–cient conditions ensuring
the existence and uniqueness of a T -periodic solution for the third-order neutral
functional difierential equation of the following form
(x(t) ¡ cx(t ¡ σ))000 + f(t; x0(t))x00(t) + g(x(t ¡ r(t)))x0(t)
+ h(t; x(t ¡ r(t))) = p(t);
where g; r; p : R ! R are continuous functions and T¡perio