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SOME RESULTS ON THE HYPER-ORDER OF SOLUTIONS OF HOMOGENE-OUS LINEAR DIFFERENTIAL EQUATIONS WITH MEROMORPHIC COEFFICIENTS


MANSOURIA SAIDANI 1 AND BENHARRAT BELA¨IDI 2
1. Department of Mathematics, Laboratory of Pure and Applied Mathematics, University of Mostaganem (UMAB), B. P. 227 Mostaganem, ALGERIA. e-mail: saidaniman@yahoo.fr
2. Department of Mathematics, Laboratory of Pure and Applied Mathematics, University of Mostaganem (UMAB), B. P. 227 Mostaganem, ALGERIA. e-mail: benharrat.belaidi@univ-mosta.dz

Issue:

SSRSMI, Number 2, Volume XXXI

Section:

Volume 31, Number 2

Abstract:

The purpose of this paper is the study of the growth of solutions of higher order linear differential equations f(k) + (Dk−1 + Bk−1eQk−1(z))f(k−1) + · · · + (D1 + B1eQ1(z)) f′ + (D0 + A1eP1(z) + A2eP2(z)) f = 0, where Ai(z) (̸≡ 0) (i = 1, 2), Bj(z) (̸≡ 0) (j = 1, ..., k − 1), Dm (z) (m = 0, ..., k−1) are meromorphic functions of finite order less than n, Pi (z) = ai,nzn+· · ·+ai,0 and Qj (z) = bj,nzn+· · ·+bj,0 are polynomials with degree n ≥ 1 such that ai,q, bj,q (i = 1, 2; j = 1, ..., k −1; q = 0, 1, ..., n) are complex numbers. Our results extend the previous results due to Habib and Bela¨ıdi [3], [11], [12] and Beddani and Hamani [4].

Keywords:

order of growth, hyper-order, exponent of convergence of zero sequence, differential equation, meromorphic function.

Code [ID]:

SSRSMI202102V31S01A0004 [0005406]

Note:

Full paper:

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