scholarly journals Further Results about a Special Fermat-Type Difference Equation

2020 ◽  
Vol 2020 ◽  
pp. 1-6
Author(s):  
Hongwei Ma ◽  
Jianming Qi ◽  
Zhenjie Zhang
Keyword(s):  
Difference Equation ◽  
Finite Order ◽  
Complex Plane ◽  
Meromorphic Solution ◽  
Unique Range Set ◽  
The Difference

In this paper, we prove the difference equation Fz3+ΔcFz+c3=1 does not have meromorphic solution of finite order over the complex plane C. We also discuss an application to the unique range set problem.

scholarly journals Meromorphic solutions of difference equations originated from Schwarzian differential equation

Filomat ◽  
2020 ◽  
Vol 34 (6) ◽  
pp. 2003-2015
Author(s):  
Shuang-Ting Lan ◽  
Zhi-Bo Huang ◽  
Chuang-Xin Chen
Keyword(s):  
Differential Equation ◽  
Positive Integer ◽  
Difference Equation ◽  
Rational Function ◽  
Finite Order ◽  
Difference Equations ◽  
Meromorphic Functions ◽  
Meromorphic Solution ◽  
Meromorphic Solutions ◽  
The Difference

Let f (z) be a meromorphic functions with finite order , R(z) be a nonconstant rational function and k be a positive integer. In this paper, we consider the difference equation originated from Schwarzian differential equation, which is of form [?3f(z)?f(z)- 3/2(?2|(z))2]k = R(z)(?f (z))2k. We investigate the uniqueness of meromorphic solution f of difference Schwarzian equation if f shares three values with any meromrphic function. The exact forms of meromorphic solutions f of difference Schwarzian equation are also presented.

scholarly journals Growth Analysis of Meromorphic Solutions of Linear Difference Equations with Entire or Meromorphic Coefficients of Finite φ-Order

Symmetry ◽  
2021 ◽  
Vol 13 (2) ◽  
pp. 267
Author(s):  
Junesang Choi ◽  
Sanjib Kumar Datta ◽  
Nityagopal Biswas
Keyword(s):  
Difference Equation ◽  
Complex Plane ◽  
Difference Equations ◽  
Growth Analysis ◽  
Meromorphic Solution ◽  
Linear Difference Equation ◽  
Meromorphic Solutions ◽  
Linear Difference Equations ◽  
Unbounded Function ◽  
Growth Properties

Many researchers’ attentions have been attracted to various growth properties of meromorphic solution f (of finite φ-order) of the following higher order linear difference equation Anzfz+n+...+A1zfz+1+A0zfz=0, where Anz,…,A0z are entire or meromorphic coefficients (of finite φ-order) in the complex plane (φ:[0,∞)→(0,∞) is a non-decreasing unbounded function). In this paper, by introducing a constant b (depending on φ) defined by lim̲r→∞logrlogφ(r)=b<∞, and we show how nicely diverse known results for the meromorphic solution f of finite φ-order of the above difference equation can be modified.

scholarly journals On zeros and growth of solutions of complex difference equations

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Min-Feng Chen ◽  
Ning Cui
Keyword(s):  
Entire Function ◽  
Difference Equation ◽  
Finite Order ◽  
Difference Equations ◽  
Meromorphic Solutions ◽  
Complex Difference ◽  
Difference Polynomial ◽  
Complex Difference Equations ◽  
The Difference ◽  
Growth Of Solutions

AbstractLet f be an entire function of finite order, let $n\geq 1$ n ≥ 1 , $m\geq 1$ m ≥ 1 , $L(z,f)\not \equiv 0$ L ( z , f ) ≢ 0 be a linear difference polynomial of f with small meromorphic coefficients, and $P_{d}(z,f)\not \equiv 0$ P d ( z , f ) ≢ 0 be a difference polynomial in f of degree $d\leq n-1$ d ≤ n − 1 with small meromorphic coefficients. We consider the growth and zeros of $f^{n}(z)L^{m}(z,f)+P_{d}(z,f)$ f n ( z ) L m ( z , f ) + P d ( z , f ) . And some counterexamples are given to show that Theorem 3.1 proved by I. Laine (J. Math. Anal. Appl. 469:808–826, 2019) is not valid. In addition, we study meromorphic solutions to the difference equation of type $f^{n}(z)+P_{d}(z,f)=p_{1}e^{\alpha _{1}z}+p_{2}e^{\alpha _{2}z}$ f n ( z ) + P d ( z , f ) = p 1 e α 1 z + p 2 e α 2 z , where $n\geq 2$ n ≥ 2 , $P_{d}(z,f)\not \equiv 0$ P d ( z , f ) ≢ 0 is a difference polynomial in f of degree $d\leq n-2$ d ≤ n − 2 with small mromorphic coefficients, $p_{i}$ p i , $\alpha _{i}$ α i ($i=1,2$ i = 1 , 2 ) are nonzero constants such that $\alpha _{1}\neq \alpha _{2}$ α 1 ≠ α 2 . Our results are improvements and complements of Laine 2019, Latreuch 2017, Liu and Mao 2018.

scholarly journals ON PROPERTIES OF FINITE-ORDER MEROMORPHIC SOLUTIONS OF A CERTAIN DIFFERENCE PAINLEVÉ I EQUATION

2011 ◽  
Vol 85 (3) ◽  
pp. 463-475 ◽  
Author(s):  
MEI-RU CHEN ◽  
ZONG-XUAN CHEN
Keyword(s):  
Finite Order ◽  
Meromorphic Solutions ◽  
Rational Solutions ◽  
Polynomial Solutions ◽  
The Difference ◽  
Image Position

AbstractIn this paper, we investigate properties of finite-order transcendental meromorphic solutions, rational solutions and polynomial solutions of the difference Painlevé I equation where a, b and c are constants, ∣a∣+∣b∣≠0.

scholarly journals On Boundedness of Solutions of the Difference Equation xn+1=(pxn+qxn−1)/(1+xn) for q>1+p>1

2009 ◽  
Vol 2009 ◽  
pp. 1-11 ◽  
Author(s):  
Hongjian Xi ◽  
Taixiang Sun ◽  
Weiyong Yu ◽  
Jinfeng Zhao
Keyword(s):  
Difference Equation ◽  
Boundedness Of Solutions ◽  
The Difference

scholarly journals An inequality with application to a difference equation

2004 ◽  
Vol 69 (3) ◽  
pp. 519-528 ◽  
Author(s):  
Jong-Yi Chen ◽  
Yunshyong Chow
Keyword(s):  
Heat Conduction ◽  
Difference Equation ◽  
Heat Conduction Problem ◽  
The Difference

In this paper we shall prove that for any 0 < d ≤ 2, holds for n ≥ 1.As an application, we shall then show that the following recursively defined sequence satisfies The difference equation above originates from a heat conduction problem studied by Myshkis (J. Difference Equ. Appl. 3(1997), 89–91).

On the difference equation

2012 ◽  
Vol 218 (11) ◽  
pp. 6291-6296 ◽  
Author(s):  
Stevo Stević
Keyword(s):  
Difference Equation ◽  
The Difference

On the difference equation xn+1=α+βxn−1e−xn

2001 ◽  
Vol 47 (7) ◽  
pp. 4623-4634 ◽  
Author(s):  
H. El-Metwally ◽  
E.A. Grove ◽  
G. Ladas ◽  
R. Levins ◽  
M. Radin
Keyword(s):  
Difference Equation ◽  
The Difference
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