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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 ...

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.

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.

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].

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