On the growth of solutions of some higher order linear differential equations

Abdallah El Farissi; Benharrat Belaidi

Displaying similar documents to “On the growth of solutions of some higher order linear differential equations”

The growth of solutions of algebraic differential equations

Walter K. Hayman (1996)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

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Suppose that $f (z)$ is a meromorphic or entire function satisfying $P (z, f, f^{'}, \dots, f^{(n)}) = 0$ where $P$ is a polynomial in all its arguments. Is there a limitation on the growth of $f$ , as measured by its characteristic $T (r, f)$ ? In general the answer to this question is not known. Theorems of Gol'dberg, Steinmetz and the author give a positive answer in certain cases. Some illustrative examples are also given.

Complex Oscillation Theory of Differential Polynomials

Abdallah El Farissi, Benharrat Belaïdi (2011)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

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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 $ρ (d_{j}) < 1$ $(j = 0, 1, 2)$ 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 $max \{ρ (A_{j}), j = 0, 1, ρ (F)\} < 1 .$

Oscillation of solutions of some higher order linear differential equations.

Xu, Hong-Yan, Cao, Ting-Bin (2009)

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

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Growth of solutions of nonhomogeneous linear differential equations.

Wang, Jun, Laine, Ilpo (2009)

Abstract and Applied Analysis

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

Belaïdi, Benharrat, Abbas, Saïd (2008)

Analele Ştiinţifice ale Universităţii “Ovidius" Constanţa. Seria: Matematică

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On unicity of meromorphic functions due to a result of Yang - Hua

Xiao-Tian Bai, Qi Han (2007)

Archivum Mathematicum

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This paper studies the unicity of meromorphic(resp. entire) functions of the form $f^{n} f^{'}$ and obtains the following main result: Let $f$ and $g$ be two non-constant meromorphic (resp. entire) functions, and let $a \in ℂ ∖ {0}$ be a non-zero finite value. Then, the condition that $E_{3)} (a, f^{n} f^{'}) = E_{3)} (a, g^{n} g^{'})$ implies that either $f = d g$ for some $(n + 1)$ -th root of unity $d$ , or $f = c_{1} e^{c z}$ and $g = c_{2} e^{- c z}$ for three non-zero constants $c$ , $c_{1}$ and $c_{2}$ with ${(c_{1} c_{2})}^{n + 1} c^{2} = - a^{2}$ provided that $n \geq 11$ (resp. $n \geq 6$ ). It improves a result of C. C. Yang and X. H. Hua. Also, some other related problems are discussed. ...