Relation between differential polynomials and small functions
type: Item
instance of: scholarly article
title: Relation between differential polynomials and small functions
zbMATH Open document ID: 1203.34148
DOI: 10.1215/0023608X-2009-019
author: Benharrat Belaïdi
author: Abdallah El Farissi
published in: Kyoto Journal of Mathematics
publication date: 2010-07-13T00:00:00Z
review text: The authors discuss the growth of solutions of the second-order non-homo\-ge\-ne\-ous differential equation \[ f'' +A_1(z)e^{az} f' +A_0(z)e^{bz} f=F, \] where \(a,b\) are complex numbers and \(A_j(z)\not\equiv 0\) \((j=0,1)\), and \(F\not\equiv 0\) are entire functions such that \(\max \{ \rho(A_0), \rho(A_1), \rho(F)\}<1 \). Slight improvements of the results of \textit{I. Laine} and \textit{J. Wang} [J. Math. Anal. Appl. 342, 39--51 (2008; Zbl 1151.34069)], and \textit{Z. X. Chen} [Sci. China Ser. A 45, No.~3, 290--300 (2002; Zbl 1054.34139)] are obtained. Relations between small functions and some differential polynomials generated by solutions of the equation are studied.
Mathematics Subject Classification ID: 34M10
Mathematics Subject Classification ID: 30D35
zbMATH DE Number: 5735956
zbMATH Keywords: growth of solutions
zbMATH Keywords: oscillation
reviewed by: Igor Chyzhykov
MaRDI profile type: Publication
cites work: Non-existence of finite order solutions of \(w''+e^{-z}w'+Q(z)w=0\)
cites work: Q3649734
cites work: Q3520080
cites work: Streng converse inequality for the F operators
cites work: Q4514593
cites work: The growth of solutions of \(f''+e^{-z}f'+Q(z)f=0\) where the order \((Q)=1\).
cites work: On the growth of solutions of a class of higher order differential equations
cites work: On the growth and fixed points of solutions of second order differential equations with meromorphic coefficients
cites work: On the Meromorphic Solutions of Non-Homogeneous Linear Differential Equations with Polynomial Coefficients
cites work: Über die subnormalen Lösungen der Differentialgleichung \(w''+e^{-z} \cdot w'+\text{konst.} \cdot w = 0\)
cites work: On the question of whether f″+ e−zf′ + B(z)f = 0 can admit a solution f ≢ 0 of finite order
cites work: Estimates for the Logarithmic Derivative of a Meromorphic Function, Plus Similar Estimates
cites work: Finite Order Solutions of Second Order Linear Differential Equations
cites work: Q5723337
cites work: The Local Growth of Power Series: A Survey of the Wiman-Valiron Method
cites work: Differential polynomials generated by linear differential equations
cites work: On complex oscillation and a problem of Ozawa
cites work: Q5291660
cites work: Q5517910
cites work: Q4405418
cites work: On a solution of \(w''+e^{-z}w'+(az+b)w=0\)
cites work: Growth of solutions of second order linear differential equations
cites work: Fixed Points and Hyper Order of Differential Polynomials Generated by Solutions of Differential Equation
full work available at URL: 0023608x-2009-019
OpenAlex ID: W1973652759
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description: scientific article; zbMATH DE number 5735956