Résumé:
In this paper, we investigate the order of growth of solutions of the higher
order linear differential equation
f
(k) +
kX−1
j=0
`
hj e
Pj
(z) + dj
´
f
(j) = 0,
where Pj (z) (j = 0, 1, . . . , k−1) are nonconstant polynomials such that deg Pj = n ≥ 1
and hj (z), dj (z) (j = 0, 1, . . . , k − 1) with h0 6≡ 0 are meromorphic functions of finite
order such that max{ρ(hj ), ρ(dj ) : j = 0, 1, . . . , k − 1} < n. We prove that every
meromorphic solution f 6≡ 0 of the above equation is of infinite order. Then, we
use the exponent of convergence of zeros or the exponent of convergence of poles of
solutions to obtain an estimation of the hyper-order of solutions.
