Results on entire and meromorphic solutions for several systems of quadratic trinomial functional equations with two complex variables

2021 ◽  
Vol 116 (1) ◽  
Author(s):  
Hong Yan Xu ◽  
Ye Yang Jiang
Keyword(s):  
Functional Equations ◽  
Complex Variables ◽  
Meromorphic Solutions ◽  
Quadratic Trinomial

Solutions for Several Quadratic Trinomial Difference Equations and Partial Differential Difference Equations in C2

Axioms ◽  
2021 ◽  
Vol 10 (2) ◽  
pp. 126
Author(s):  
Hong Li ◽  
Hongyan Xu
Keyword(s):  
Positive Integer ◽  
Finite Order ◽  
Difference Equations ◽  
Functional Equations ◽  
Growth Order ◽  
Entire Solutions ◽  
Partial Differential ◽  
Integer Order ◽  
Significant Difference ◽  
Quadratic Trinomial

This article is to investigate the existence of entire solutions of several quadratic trinomial difference equations f(z+c)2+2αf(z)f(z+c)+f(z)2=eg(z), and the partial differential difference equations f(z+c)2+2αf(z+c)∂f(z)∂z1+∂f(z)∂z12=eg(z),f(z+c)2+2αf(z+c)∂f(z)∂z1+∂f(z)∂z2+∂f(z)∂z1+∂f(z)∂z22=eg(z). We establish some theorems about the forms of the finite order transcendental entire solutions of these functional equations. We also list a series of examples to explain the existence of the finite order transcendental entire solutions of such equations. Meantime, some examples show that there exists a very significant difference with the previous literature on the growth order of the finite order transcendental entire solutions. Our results show that some functional equations can admit the transcendental entire solutions with any positive integer order. These results make a few improvements of the previous theorems given by Xu and Cao, Liu and Yang.

scholarly journals Correction to “Meromorphic solutions of some functional equations”

1999 ◽  
Vol 6 (4) ◽  
pp. 617-618 ◽  
Author(s):  
Walter Bergweiler ◽  
Katsuya Ishizaki ◽  
Niro Yanagihara
Keyword(s):  
Functional Equations ◽  
Meromorphic Solutions

scholarly journals Meromorphic solutions of some functional equations

1998 ◽  
Vol 5 (3) ◽  
pp. 248-258 ◽  
Author(s):  
Walter Bergweiler ◽  
Katsuya Ishizaki ◽  
Niro Yanagihara
Keyword(s):  
Functional Equations ◽  
Meromorphic Solutions

scholarly journals The Existence of Meromorphic Solutions of Some Types of Systems of Complex Functional Equations

2015 ◽  
Vol 2015 ◽  
pp. 1-10 ◽  
Author(s):  
Hong-Yan Xu ◽  
Jin-Lian Wang ◽  
Hua Wang
Keyword(s):  
Functional Equations ◽  
Meromorphic Solutions ◽  
Complex Functional Equations

We investigate the existence of transcendental meromorphic solutions of some types of systems of complex functional equations and obtain some results about the existence of meromorphic solutions of such systems. Our results are improvement of the previous theorems given by Gao, Xu, and Zheng, and our examples show that our results are sharp to some extent.

scholarly journals On the growth of compositions of linear and meromorphic functions

1991 ◽  
Vol 44 (2) ◽  
pp. 263-269 ◽  
Author(s):  
Jianyong Qiao
Keyword(s):  
Meromorphic Function ◽  
Asymptotic Behaviour ◽  
Functional Equations ◽  
Meromorphic Functions ◽  
Meromorphic Solutions

Let f(z) be a meromorphic function; we shall investigate the asymptotic behaviour of the ratio T(r, f(z + α))/T(r, f(z)) and T(r, f(αz))/T(r, f(z)), and discuss the growth of the meromorphic solutions of some functional equations.

Sign in / Sign up

Export Citation Format

Share Document