Résumé:
In this thesis, we con rmed the usefulness of powerful Nevanlinna theory tools such as the charac-
teristic function and the rst fundamental theorem of Nevanlinna. These techniques helped us to
improve on several results obtained by other researchers concerning the following linear di⁄erential
equations
(k)
(k 1)
0
f + A (z)f
+ + A (z)f + A (z)f = 0;
1
0
k 1
where A (z) are analytic or meromorphic in the unit disc = fz : jzj < 1g, i = 0; 1; :::; k 1; k 2.
i
In the rst instance, when A dominates the other coe¢ cients near a point on the boundary of
0
; we gave the statement of theorems of Hamouda.
Secondly, we investigated the growth of solutions of di⁄erential linear equations of [p; q]-order.
In the nal stages of this project, we considered generalizing some of the above-mentioned results
by assuming A dominates the other coe¢ cients near a point on the boundary of .
s
A natural question: Is it possible to generalize the results of previous theorems if the equation is
non-homogeneous? If we look at the linear di⁄erential equations of the following form
(k)
(k 1)
0
f + A (z)f
+ + A (z)f + A (z)f = K(z);
1
0
k 1
where A (z); K(z) are analytic or meromorphic functions in the unit disc = fz : jzj < 1g,
i = 0; 1; :::; k 1; k 2.
i
Is it possible to use the same approach as in this thesis and Hamouda s paper, namely that one
coe¢ cient dominates the other coe¢ cients near a point on the boundary of ?
Can we improve the results found in this thesis when the coe¢ cients A (z) are entire functions?
