On the Order of Growth of Solutions to Complex Non-homogeneous Linear Differential Equations

Habib Habib; Benharrat Belaïdi

doi:10.5666/KMJ.2016.56.3.819

Articles

Kyungpook Mathematical Journal -0001; 56(3): 819-829

Published online November 30, -0001

On the Order of Growth of Solutions to Complex Non-homogeneous Linear Differential Equations

Habib Habib¹, Benharrat Belaïdi²

Department of Mathematics, Laboratory of Biomathematics, University of Sidi Bel Abbes, B. P. 89 Sidi Bel Abbes, Algeria¹
Department of Mathematics, Laboratory of Pure and Applied Mathematics, University of Mostaganem (UMAB), B. P. 227 Mostaganem, Algeria²

Received: March 21, 2015; Accepted: July 29, 2016

Abstract

Go to

Abstract

In this paper, we study the order of growth of solutions to the non-homogeneous linear differential equation f(k)+Ak-1eazf(k-1)+⋯+A1eazf′+A0eazf=F1eaz+F2ebz,

where A_j (z) (≢ 0) (j = 0, 1, · · ·, k − 1), F_j (z) (≢ 0) (j = 1, 2) are entire functions and a, b are complex numbers such that ab (a − b) ≠ 0.

Keywords:

Differential equation, characteristic function, ,entire function, exponent of convergence of the sequence of zeros, order of ,growth.