On meromorphic solutions of a type of system of composite functional equations

doi:10.1016/S0252-9602(12)60060-5

Acta Mathematica Scientia

Volume 32, Issue 2, March 2012, Pages 800-806

https://doi.org/10.1016/S0252-9602(12)60060-5 Get rights and content

Abstract

In this article, we mainly investigate the growth and existence of meromorphic solutions of a type of systems of composite functional equations, and obtain some interesting results. It extends some results concerning functional equations to the systems of functional equations.

References (26)

Zongxuan Chen et al.
On the growth of solutions of a class of higher order differential equations
Acta Mathematica Scientia
(2004)
Lingyun Gao
On the growth of solutions of higher-order differential equations
Acta Mathematica Scientia
(2002)
Hongxun Yi et al.
Theory of the uniqueness of meromorphic functions (in Chinese)
(1995)
I Laine
Nevanlinna theory and complex differential equations
(1993)
R Goldstein
On certain compositions of functions of a complex variable
Aequations Math
(1970)
R Goldstein
On meromorphic solutions of a functional equations
Aequations Math
(1972)
R Goldstein
On meromorphic solutions of certain functional equations
Aequations Math
(1978)
R Goldstein
Some results on factorisation of meromorphic functions
J London Math Soc
(1971)
Bergweiler W. Untersuchungen des Wachstums Zusammengesetzter meromorpher Funktionen [Dissertation]. Aachen,...
W Bergweiler et al.
Growth of meromorphic solutions of some functional equations I
Aequations Math
(2002)

W Bergweiler et al.

Meromorphic solutions of some functional equations

Methods Appl Anal

(1998)

J Heittokangas et al.

Meromorphic solutions of some linear functional equations

Aequations Math

(2000)

H Silvennoinen

Meromorphic solutions of some composite functional equations

Ann Acad Sci Fenn, Mathematica Dissertations, Helsinki

(2003)

Cited by (19)

Riccati-type result for meromorphic solutions of systems of composite functional equations
2017, Acta Mathematica Scientia
By use of Nevanlinna value distribution theory, we will investigate the properties of meromorphic solutions of two types of systems of composite functional equations and obtain some results. One of the results we get is about both components of meromorphic solutions on the system of composite functional equations satisfying Riccati differential equation, the other one is property of meromorphic solutions of the other system of composite functional equations while restricting the growth.
On entire solutions of two types of systems of complex differential-difference equations
2017, Acta Mathematica Scientia
Meromorphic solutions of a type of system of complex differential-difference equations
2015, Acta Mathematica Scientia
Applying Nevanlinna theory of the value distribution of meromorphic functions, we mainly study the growth and some other properties of meromorphic solutions of the type of system of complex differential and difference equations of the following form where λ_ij (j = 1,2,···, n; i = 1,2) are finite non-negative integers, and c_j (j = 1,2,·,n) are distinct, nonzero complex numbers, α_j(z), β_j(z) (j = 1,2,·,n) are small functions relative to f_i(z) (i = 1,2) respectively, R_i(z,f(z)) (i = 1,2) are rational in f_i(z) (i = 1,2) with coefficients which are small functions of f_i(z)(i = 1,2) respectively.
The growth order of solutions of systems of complex difference equations
2013, Acta Mathematica Scientia
Estimates of N-function and m-function of meromorphic solutions of systems of complex difference equations
2012, Acta Mathematica Scientia
We apply Nevanlinna theory of the value distribution of meromorphic functions to study the properties of Nevanlinna counting function and proximity function of meromorphic solutions of a type of systems of complex difference equations. Our results can give estimates on the proximity function and the counting function of solutions of systems of difference equations. This implies that solutions have a relatively large number of poles. It extend some result concerning difference equations to the systems of difference equations.
The existence of entire solutions of some systems of the Fermat type differential-difference equations
2022, AIMS Mathematics

View all citing articles on Scopus

: Project supported by NSF of China (10471065) and the Natural Science Foundation of Guangdong Province (04010474).

View full text

On meromorphic solutions of a type of system of composite functional equations

Abstract

Acta Mathematica Scientia

Acta Mathematica Scientia

Theory of the uniqueness of meromorphic functions (in Chinese)

Nevanlinna theory and complex differential equations

On certain compositions of functions of a complex variable

Aequations Math

On meromorphic solutions of a functional equations

Aequations Math

On meromorphic solutions of certain functional equations

Aequations Math

Some results on factorisation of meromorphic functions

J London Math Soc

Growth of meromorphic solutions of some functional equations I

Aequations Math

Meromorphic solutions of some functional equations

Methods Appl Anal

Meromorphic solutions of some linear functional equations

Aequations Math

Meromorphic solutions of some composite functional equations

Ann Acad Sci Fenn, Mathematica Dissertations, Helsinki