EUDML

This paper is devoted to considering the iterated order and the fixed points of some differential polynomials generated by solutions of the differential equation $f^{^{''}} + A_{1} (z) f^{^{'}} + A_{0} (z) f = F,$ where $A_{1} (z)$ , $A_{0} (z)$ $(\neg \equiv 0)$ , $F$ are meromorphic functions of finite iterated $p$ -order.

On open problems of F. Qi.

Belaidi, Benharrat; El Farissi, Abdallah; Latreuch, Zinelaâbidine — 2009

JIPAM. Journal of Inequalities in Pure & Applied Mathematics [electronic only]

Growth and oscillation of differential polynomials in the unit disc.

El Farissi, Abdallah; Belaidi, Benharrat; Latreuch, Zinelaabidine — 2010

Electronic Journal of Differential Equations (EJDE) [electronic only]

Growth and oscillation theory of solutions of some linear differential equations

Benharrat Belaidi — 2008

Matematički Vesnik

Complex Oscillation of Differential Polynomials Generated by Meromorphic Solutions of Linear Differential Equations

Benharrat Belaïdi — 2011

Publications de l'Institut Mathématique

Growth and fixed points of meromorphic solutions of higher order linear differential equations

Habib Habib; Benharrat Belaïdi — 2013

Annales Polonici Mathematici

We investigate the growth and fixed points of meromorphic solutions of higher order linear differential equations with meromorphic coefficients and their derivatives. Our results extend the previous results due to Peng and Chen.

Some Results on the Properties of Differential Polynomials Generated by Solutionsof Complex Differential Equations

Zinelâabidine LATREUCH; Benharrat BELAÏDI — 2015

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

This paper is devoted to considering the complex oscillation of differential polynomials generated by meromorphic solutions of the differential equation $f^{(k)} + A_{k - 1} (z) f^{(k - 1)} + \dots + A_{1} (z) f^{'} + A_{0} (z) f = 0,$ where $A_{i} (z)$ $(i = 0, 1, \dots, k - 1)$ are meromorphic functions of finite order in the complex plane.

Zeros of Solutions and Their Derivatives of Higher Order Non-homogeneous Linear Differential Equations

Benharrat Belaidi; Zinelâabidine Latreuch — 2015

Communications in Mathematics

This paper is devoted to studying the growth and oscillation of solutions and their derivatives of higher order non-homogeneous linear differential equations with finite order meromorphic coefficients. Illustrative examples are also treated.

Growth and oscillation of some class of differential polynomials in the unit disc

Benharrat Belaïdi — 2011

Kragujevac Journal of Mathematics

Complex Oscillation Theory of Differential Polynomials

Abdallah El Farissi; Benharrat Belaïdi — 2011

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

In this paper, we investigate the relationship between small functions and differential polynomials $g_{f} (z) = d_{2} f^{''} + d_{1} f^{'} + d_{0} f$ , where $d_{0} (z)$ , $d_{1} (z)$ , $d_{2} (z)$ are entire functions that are not all equal to zero with $ρ (d_{j}) < 1$ $(j = 0, 1, 2)$ generated by solutions of the differential equation $f^{''} + A_{1} (z) e^{a z} f^{'} + A_{0} (z) e^{b z} f = F$ , where $a, b$ are complex numbers that satisfy $a b (a - b) \neq 0$ and $A_{j} (z) \neg \equiv 0$ ( $j = 0, 1$ ), $F (z) \neg \equiv 0$ are entire functions such that $max \{ρ (A_{j}), j = 0, 1, ρ (F)\} < 1 .$

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Oscillation of fast growing solutions of linear differential equations in the unit disc.

On the iterated order and the fixed points of entire solutions of some complex linear differential equations.

Some precise estimates of the hyper order of solutions of some complex linear differential equations.

Growth of solutions of certain non-homogeneous linear differential equations with entire coefficients.

Estimation of the hyper-order of entire solutions of complex linear ordinary differential equations whose coefficients are entire functions.

Growth and oscillation of solutions to linear differential equations with entire coefficients having the same order.

Some results on the complex oscillation theory of differential equations with polynomial coefficients.

On the hyper order of solutions of a class of higher order linear differential equations.

Order and hyper-order of entire solutions of linear differential equations with entire coefficients.

Some results on the complex oscillation theory of some differential polynomials.

The fixed points and iterated order of some differential polynomials