scholarly journals Unicity of Meromorphic Solutions of the Pielou Logistic Equation

2020 ◽  
Vol 2020 ◽  
pp. 1-5
Author(s):  
Sheng Li ◽  
Baoqin Chen
Keyword(s):  
Finite Order ◽  
Meromorphic Solution ◽  
Logistic Equation ◽  
Meromorphic Solutions

This paper mainly considers the unicity of meromorphic solutions of the Pielou logistic equation yz+1=Rzyz/Qz+Pzyz, where Pz,Qz, and Rz are nonzero polynomials. It shows that the finite order transcendental meromorphic solution of the Pielou logistic equation is mainly determined by its poles and 1-value points. Examples are given for the sharpness of our result.

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 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.

A note on meromorphic functions with finite order and of bounded l-index

2021 ◽  
Vol 18 (1) ◽  
pp. 1-11
Author(s):  
Andriy Bandura
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Finite Order ◽  
General Problem ◽  
Meromorphic Functions ◽  
Entire Functions ◽  
Sufficient Conditions ◽  
Meromorphic Solutions ◽  
Entire Solutions ◽  
Riccati Differential Equation

We present a generalization of concept of bounded $l$-index for meromorphic functions of finite order. Using known results for entire functions of bounded $l$-index we obtain similar propositions for meromorphic functions. There are presented analogs of Hayman's theorem and logarithmic criterion for this class. The propositions are widely used to investigate $l$-index boundedness of entire solutions of differential equations. Taking this into account we raise a general problem of generalization of some results from theory of entire functions of bounded $l$-index by meromorphic functions of finite order and their applications to meromorphic solutions of differential equations. There are deduced sufficient conditions providing $l$-index boundedness of meromoprhic solutions of finite order for the Riccati differential equation. Also we proved that the Weierstrass $\wp$-function has bounded $l$-index with $l(z)=|z|.$

scholarly journals Order of growth of solutions to algebraic differential equations in the unit disk

2004 ◽  
Vol 2004 (41) ◽  
pp. 2161-2170 ◽  
Author(s):  
D. Benbourenane ◽  
L. R. Sons
Keyword(s):  
Differential Equations ◽  
Unit Disk ◽  
Finite Order ◽  
Meromorphic Solutions ◽  
Order Of Growth ◽  
Growth Estimate ◽  
Algebraic Differential Equations ◽  
Uniform Growth ◽  
Growth Of Solutions

S. B. Bank has shown that there is no uniform growth estimate for meromorphic solutions of algebraic differential equations with meromorphic coefficients in the unit disk. We give conditions under which such solutions must have a finite order of growth.

scholarly journals Uniqueness for meromorphic solutions of Schwarzian differential equation

2021 ◽  
Vol 6 (11) ◽  
pp. 12619-12631
Author(s):  
Dan-Gui Yao ◽  
◽  
Zhi-Bo Huang ◽  
Ran-Ran Zhang ◽  
Keyword(s):  
Differential Equation ◽  
Positive Integer ◽  
Meromorphic Function ◽  
Rational Function ◽  
Meromorphic Solution ◽  
Meromorphic Solutions

<abstract><p>Let $ f $ be a meromorphic function, $ R $ be a nonconstant rational function and $ k $ be a positive integer. In this paper, we consider the Schwarzian differential equation of the form</p> <p><disp-formula> <label/> <tex-math id="FE1"> \begin{document}$ \begin{align*} \left[\frac{f'''}{f'}-\frac{3}{2}\left(\frac{f''}{f'}\right)^{2}\right]^{k} = R(z). \end{align*} $\end{document} </tex-math></disp-formula></p> <p>We investigate the uniqueness of meromorphic solutions of the above Schwarzian differential equation if the meromorphic solution $ f $ shares three values with any other meromorphic function.</p></abstract>

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 Linear Difference Equations with Polynomial Coefficients

2017 ◽  
Vol 59 (1) ◽  
pp. 159-168
Author(s):  
Y. Zhang ◽  
Z. Gao ◽  
H. Zhang
Keyword(s):  
Difference Equation ◽  
Difference Equations ◽  
Necessary Conditions ◽  
Meromorphic Solution ◽  
Linear Difference Equation ◽  
Meromorphic Solutions ◽  
Linear Difference Equations ◽  
Polynomial Coefficients ◽  
Difference Analogue ◽  
Borel Exceptional Values

AbstractWe study the growth of the transcendental meromorphic solution f(z) of the linear difference equation:where q(z), p0(z), ..., pn-(z) (n ≥ 1) are polynomials such that p0(z)pn(z) ≢ 0, and obtain some necessary conditions guaranteeing that the order of f(z) satisfies σ(f) ≥ 1 using a difference analogue of the Wiman-Valiron theory. Moreover, we give the form of f(z) with two Borel exceptional values when two of p0(z), ..., pn(z) have the maximal degrees.

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