scholarly journals On Properties of meromorphic solutions of difference Painlevé I and II equation

2017 ◽  
Vol 5 (2) ◽  
pp. 37
Author(s):  
Weimin Xue ◽  
Yanmei Teng
Keyword(s):  
Fixed Points ◽  
Finite Order ◽  
Divided Difference ◽  
Meromorphic Solutions

In this paper, we investigate some properties of finite order transcendental meromorphic solutions of difference Painlev \(\)\acute{e}\) I and II equations, and obtain precise estimations of exponents of convergence of poles of difference \(\)\Delta w(z)=w(z+1)-w(z)\) and divided difference \(\)\frac{\Delta w(z)}{w(z)}\), and of fixed points of \(\)w(z+\eta)$ ($\eta\in \mathbb{C}\setminus\{0\}\)).

scholarly journals The properties of solutions for several types of Painlevé equations concerning fixed-points, zeros and poles

2019 ◽  
Vol 17 (1) ◽  
pp. 1014-1024
Author(s):  
Hong Yan Xu ◽  
Xiu Min Zheng
Keyword(s):  
Fixed Points ◽  
Difference Equations ◽  
Painlevé Equations ◽  
Meromorphic Solutions ◽  
Painleve Equations ◽  
Zeros And Poles

Abstract The purpose of this manuscript is to study some properties on meromorphic solutions for several types of q-difference equations. Some exponents of convergence of zeros, poles and fixed points related to meromorphic solutions for some q-difference equations are obtained. Our theorems are some extension and improvements to those results given by Qi, Peng, Chen, and Zhang.

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.

Fixed Points of Automorphisms of Free Pro-p Groups of Rank 2

1995 ◽  
Vol 47 (2) ◽  
pp. 383-404 ◽  
Author(s):  
Wolfgang N. Herfort ◽  
Luis Ribes ◽  
Pavel A. Zalesskii
Keyword(s):  
Fixed Points ◽  
Prime Number ◽  
Finite Order ◽  
Finite Power ◽  
Rank 2

AbstractLet p be a prime number, and let F be a free pro-p group of rank two. Consider an automorphism α of F of finite order m, and let FixF(α) = {x ∈ F | α(x) = x} be the subgroup of F consisting of the elements fixed by α. It is known that if m is prime to p and α = idF, then the rank of FixF(α) is infinite. In this paper we show that if m is a finite power pr of p, the rank of FixF(α) is at most 2. We conjecture that if the rank of F is n and the order of a is a power of α, then rank (FixF(α)) ≤ n.

scholarly journals ON SOME PROJECTION METHODS FOR APPROXIMATING FIXED POINTS OF NONLINEAR EQUATIONS IN BANACH SPACE

1990 ◽  
Vol 21 (4) ◽  
pp. 351-357
Author(s):  
IOANNIS K. ARGYROS
Keyword(s):  
Banach Space ◽  
Fixed Point ◽  
Linear Operator ◽  
Fixed Points ◽  
Finite Order ◽  
Operator Equation ◽  
Algebraic System ◽  
Projection Methods ◽  
Linear Algebraic System ◽  
Non Linear Operator

We use a Newton-like method to approximate a fixed point of a non- linear operator equation in a Banach space. Our iterates are computed at each step by solving a linear algebraic system of finite order.

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