Kyoto Journal of Mathematics

Relation between differential polynomials and small functions

Benharrat Belaïdi and Abdallah El Farissi

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Abstract

In this article, we discuss the growth of solutions of the second-order nonhomogeneous linear differential equation

f+A1(z)eazf+A0(z)ebzf=F,

where a, b are complex constants and Aj(z)0 (j=0,1), and F0 are entire functions such that max{ρ(Aj)(j=0,1),ρ(F)}<1. We also investigate the relationship between small functions and differential polynomials gf(z)=d2f+d1f+d0f, where d0(z),d1(z),d2(z) are entire functions that are not all equal to zero with ρ(dj)<1 (j=0,1,2) generated by solutions of the above equation.

Article information

Source
Kyoto J. Math., Volume 50, Number 2 (2010), 453-468.

Dates
First available in Project Euclid: 7 May 2010

Permanent link to this document
https://projecteuclid.org/euclid.kjm/1273236822

Digital Object Identifier
doi:10.1215/0023608X-2009-019

Mathematical Reviews number (MathSciNet)
MR2666664

Zentralblatt MATH identifier
1203.34148

Subjects
Primary: 34M10: Oscillation, growth of solutions
Secondary: 30D35: Distribution of values, Nevanlinna theory

Citation

Belaïdi, Benharrat; El Farissi, Abdallah. Relation between differential polynomials and small functions. Kyoto J. Math. 50 (2010), no. 2, 453--468. doi:10.1215/0023608X-2009-019. https://projecteuclid.org/euclid.kjm/1273236822


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