ON THE GROWTH OF SOLUTIONS OF HOMOGENEOUS AND NON-HOMOGENEOUS LINEAR DIFFERENTIAL EQUATIONS WITH MEROMORPHIC COEFFICIENTS
MANSOURIA SAIDANI, BENHARRAT BELAȈDI
Department of Mathematics, Laboratory of Pure and Applied Mathematics, University of Mostaganem (UMAB), B. P. 227 Mostaganem-Algeria. e-mails: saidaniman@yahoo.fr; benharrat.belaidi@univ-mosta.dz
Abstract
In this paper, we investigate the growth of solutions of higher order linear differential equations
f^{(k)}+A_{k-1}(z)f^{(k-1)}+⋯+A₁(z)f′+A₀(z)f=0
and
f^{(k)}+A_{k-1}(z)f^{(k-1)}+⋯+A₁(z)f′+A₀(z)f=F(z),
where A₀(z)≡0, A₁(z),⋯,A_{k-1}(z) and F(z)≡0 are meromorphic functions of finite iterated p-order. We improve and extend some results of papers [1] and [5] by using the concept of the iterated order and considering the growth of some arbitrary dominant coefficient A_{s} (s=0,1,⋯,k-1) instead of A₀.