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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 $ρ (d_{j}) < 1$ $(j = 0, 1 ...$

Differential analogues of the Brück conjecture

Xiao-Guang Qi, Lian-Zhong Yang (2011)

Annales Polonici Mathematici

We give some growth properties for solutions of linear complex differential equations which are closely related to the Brück Conjecture. We also prove that the Brück Conjecture holds when certain proximity functions are relatively small.

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

Belaïdi, Benharrat (2002)

Electronic Journal of Qualitative Theory of Differential Equations [electronic only]

Finite and infinite order of growth of solutions to linear differential equations near a singular point

Samir Cherief, Saada Hamouda (2021)

Mathematica Bohemica

In this paper, we investigate the growth of solutions of a certain class of linear differential equation where the coefficients are analytic functions in the closed complex plane except at a finite singular point. For that, we will use the value distribution theory of meromorphic functions developed by Rolf Nevanlinna with adapted definitions.

Finite order solutions of complex linear differential equations.

Laine, Ilpo, Yang, Ronghua (2004)

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

Global properties of the Painlevé transcendents: new results and open questions.

Steinmetz, Norbert (2005)

Annales Academiae Scientiarum Fennicae. Mathematica

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.

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

Belaidi, Benharrat (2009)

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

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

Benharrat Belaïdi (2011)

Kragujevac Journal of Mathematics

Growth and oscillation theory of solutions of some linear differential equations

Benharrat Belaidi (2008)

Matematički Vesnik

Growth estimates for solutions of linear complex differential equations.

Heittokangas, J., Korhonen, R., Rättyä, J. (2004)

Annales Academiae Scientiarum Fennicae. Mathematica

Growth of meromorphic solutions of higher-order linear differential equations.

Chen, Wenjuan, Xu, Junfeng (2009)

Electronic Journal of Qualitative Theory of Differential Equations [electronic only]

Growth of solutions of a class of complex differential equations

Ting-Bin Cao (2009)

Annales Polonici Mathematici

The main purpose of this paper is to partly answer a question of L. Z. Yang [Israel J. Math. 147 (2005), 359-370] by proving that every entire solution f of the differential equation $f^{'} - e^{P (z)} f = 1$ has infinite order and its hyperorder is a positive integer or infinity, where P is a nonconstant entire function of order less than 1/2. As an application, we obtain a uniqueness theorem for entire functions related to a conjecture of Brück [Results Math. 30 (1996), 21-24].

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

Belaïdi, Benharrat (2004)

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

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