Entire solutions of q-difference equations and value distribution of q-difference polynomials

2013 ◽  
Vol 109 (1) ◽  
pp. 39-46 ◽  
Author(s):  
Jilong Zhang ◽  
Lianzhong Yang
Keyword(s):  
Difference Equations ◽  
Value Distribution ◽  
Entire Solutions ◽  
Difference Polynomials

On Properties of Entire Solutions of Difference Equations and Difference Polynomials

2015 ◽  
Vol 65 (3) ◽  
Author(s):  
Xiaoguang Qi ◽  
Yinhong Cao ◽  
Yong Liu
Keyword(s):  
Difference Equation ◽  
Difference Equations ◽  
Linear Difference Equation ◽  
Entire Solutions ◽  
Non Linear ◽  
Difference Polynomials

AbstractIn this paper, we consider the existence of entire solutions of certain type of non-linear difference equation of the form: f(z)

Some results for complex partial q-difference equations in ℂ n \mathbb{C}^{n}

2019 ◽  
Vol 26 (3) ◽  
pp. 471-481
Author(s):  
Yue Wang
Keyword(s):  
Difference Equations ◽  
Nevanlinna Theory ◽  
Meromorphic Functions ◽  
Zero Order ◽  
Value Distribution ◽  
Meromorphic Solutions ◽  
Difference Polynomials

Abstract Using the Nevanlinna theory of the value distribution of meromorphic functions, the value distribution of complex partial q-difference polynomials of meromorphic functions of zero order is investigated. The existence of meromorphic solutions of some types of systems of complex partial q-difference equations in {\mathbb{C}^{n}} is also investigated. Improvements and extensions of some results in the literature are presented. Some examples show that our results are, in a certain sense, the best possible.

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 A NOTE ON VALUE DISTRIBUTION OF DIFFERENCE POLYNOMIALS

2010 ◽  
Vol 81 (3) ◽  
pp. 353-360 ◽  
Author(s):  
K. LIU ◽  
I. LAINE
Keyword(s):  
Value Distribution ◽  
Difference Polynomials ◽  
Brück Conjecture

AbstractIn this paper, we investigate the value distribution of difference polynomials and prove some difference analogues of results of Hayman and the Brück conjecture.

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