Résumé:
Throughout this work, by using a generalized concept of order called ϕ-order, we have
discussed the possibility of extendingsome results about the growth ofmeromorphic so-
lutions to linear differential equations of the form:
(k)
(k−1)
0
A (z) f +A
(z) f
+ · · ·+A (z) f +A (z) f = 0
(3.26)
1
0
k
k−1
(k)
(k−1)
0
A (z) f +A
(z) f
+ · · ·+A (z) f +A (z) f = F (z) ,
where A and F aremeromorphic functions of finite [p,q ]−ϕ order.
(3.27)
1
0
k
k−1
j
We have obtained the relationship between the solutions and the meromorphic coeffi-
cients in terms of ϕ-order, estimations about the [p,q ]−ϕ order and the [p,q ]−ϕ con-
vergence exponent of the solutions to such equations.
Now, some open questions and problems are proposed.
Problem 1. Can we get the similar result using the (α,β,ν) -order defined in [3]? In other
words what can be said about the growth of solutions of the differential equations (3.26)
and (3.27) if the coefficients aremeromorphic functions of (α,β,ν) -order?
Problem 2. What are the hypothesis on the dominant coefficient that guarantee that the
solutions of the above equations have a finite (α,β,ν) -order?
