Department of Mathematics, Faculty of Science, Okayama University
Doi
Abstract
This paper is devoted to studying the growth of solutions
of the higher order nonhomogeneous linear differential equation
f(k) + Ak−1f(k−1) + ... + A2f
"
+ (D1 (z) + A1 (z) eP(z)) f
'
+ (D0 (z) + A0 (z)e Q(z)) f = F (k ≥ 2) ,
where P (z) , Q(z) are nonconstant polynomials such that deg P =
degQ = n and Aj (z) (j = 0, 1, ..., k − 1) , F (z) are entire functions
with max{p(Aj) (j = 0, 1, ..., k − 1) , p(Dj) (j = 0, 1)} < n. We also
investigate the relationship between small functions and the solutions of
the above equation
