Taiwanese Journal of Mathematics

GROWTH AND DIFFERENCE PROPERTIES OF MEROMORPHIC SOLUTIONS ON DIFFERENCE EQUATIONS

Zong-Xuan Chen and Kwang Ho Shon

Full-text: Open access

Abstract

Consider the difference Riccati equation $f(z+1)=\frac{a(z)f(z)+b(z)}{c(z)f(z)+d(z)}$, where  $a,~b,~c,~d$ are polynomials, we precisely estimate  growth of meromorphic solutions. To the difference Riccati equation $f(z+1)=\frac{A(z)+f(z)}{1-f(z)}$, where $A(z)=\frac{m(z)}{n(z)},$  $m(z),~n(z)$ are irreducible nonconstant polynomials, we precisely estimate exponents of convergence of zeros and poles of  meromorphic solutions $f(z)$, their differences $\Delta f(z)=f(z+1)-f(z)$ and divided differences $\frac{\Delta f(z)}{f(z)}$.

Article information

Source
Taiwanese J. Math., Volume 19, Number 5 (2015), 1401-1414.

Dates
First available in Project Euclid: 4 July 2017

Permanent link to this document
https://projecteuclid.org/euclid.twjm/1499133716

Digital Object Identifier
doi:10.11650/tjm.19.2015.5547

Mathematical Reviews number (MathSciNet)
MR3412013

Zentralblatt MATH identifier
1361.30047

Subjects
Primary: 30D35: Distribution of values, Nevanlinna theory 39A10: Difference equations, additive

Keywords
difference Riccati equation growth order zero pole

Citation

Chen, Zong-Xuan; Shon, Kwang Ho. GROWTH AND DIFFERENCE PROPERTIES OF MEROMORPHIC SOLUTIONS ON DIFFERENCE EQUATIONS. Taiwanese J. Math. 19 (2015), no. 5, 1401--1414. doi:10.11650/tjm.19.2015.5547. https://projecteuclid.org/euclid.twjm/1499133716


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