<abstract xmlns="http://www.w3.org/1999/xhtml"> In this paper, we investigate the order and the hyper-order of growth of solutions of the linear differential equation <disp-formula><inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="../graphic/auom_35_Fig_1.png"></inline-graphic></disp-formula> where n≥2 is an integer, Aj (z) (≢0) (j = 1,2) are entire functions with max {σ A(j) : (j = 1,2} &lt; 1, Q (z) = qmzm + ... + q1z + q0 is a nonoonstant polynomial and a1, a2 are complex numbers. Under some conditions, we prove that every solution f (z) ≢ 0 of the above equation is of infinite order and hyper-order 1. </abstract>

In this paper, we investigate the order and the hyper-order of growth of solutions of the linear differential equation where n≥2 is an integer, Aj (z) (≢0) (j = 1,2) are entire functions with max {σ A(j) : (j = 1,2} < 1, Q (z) = qmzm + ... + q1z + q0 is a nonoonstant polynomial and a1, a2 are complex numbers. Under some conditions, we prove that every solution f (z) ≢ 0 of the above equation is of infinite order and hyper-order 1.

On the Growth of Solutions of Some Second Order Linear Differential Equations with Entire Coefficients

Department of Mathematics, Laboratory of Pure and Applied Mathematics University of Mostaganem (UMAB), B. P. 227 Mostaganem-Algeria

Analele ştiinţifice ale Universităţii "Ovidius" Constanţa. Seria Matematică

In this paper, we investigate the order and the hyper-order of growth of solutions of the linear differential equation  where n≥2 is an integer, Aj (z) (≢0) (j...

On the Growth of Solutions of Some Second Order Linear Differential Equations with Entire Coefficients

Published Online: Sep 19, 2013

Page range: 35 - 52

DOI: https://doi.org/10.2478/auom-2013-0022

Keywords
Linear differential equations, Entire solutions, Order of growth, Hyperorder, Fixed points

This content is open access.

On the Growth of Solutions of Some Second Order Linear Differential Equations with Entire Coefficients

Published Online: Sep 19, 2013

Page range: 35 - 52

DOI: https://doi.org/10.2478/auom-2013-0022

KeywordsLinear differential equations, Entire solutions, Order of growth, Hyperorder, Fixed points

This content is open access.

Keywords
Linear differential equations, Entire solutions, Order of growth, Hyperorder, Fixed points