# Zeros, Poles, and Fixed Points of Meromorphic Solutions of Difference PainlevÃ© Equations

## Related Articles

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In this paper, we mainly investigate properties of finite order transcendental meromorphic solutions of difference PainlevÃ© equations. If f is a finite order transcendental meromorphic solution of difference PainlevÃ© equations, then we get some estimates of the order and the exponent of...

- Lower estimates of the growth order of solutions to the second PainlevÃ© hierarchy. Sasaki, Yoshikatsu // Journal of Mathematical Physics;Jul2013, Vol. 54 Issue 7, p073510
This article concerns with the second PainlevÃ© hierarchy, i.e., the 2nth order analogues of the second PainlevÃ© equation. Though several higher order analogues of the second PainlevÃ© equation are proposed by several authors, we investigate one derived from the KdV hierarchy by...

- A General Family of Two Step Collocation Methods for Ordinary Differential Equations. D'Ambrosio, R.; Ferro, M.; Paternoster, B. // AIP Conference Proceedings;9/6/2007, Vol. 936 Issue 1, p45
We consider a general family of two step collocation methods for the numerical integration of Ordinary Differential Equations, which depends on the stage values at two consecutive step points. We describe two constructive techniques, discuss the order of the resulting methods, compute the nodes...

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The numerical solution of initial value problems for linear fractional differential equations is considered. The derivatives of the given functions may be unbounded at the initial point of the interval of integration. Using an integral equation reformulation and special graded grids, global...

- Value Distribution of Differences of Meromorphic Functions. Xiumin Zheng; Zongxuan Chen // Southeast Asian Bulletin of Mathematics;2013, Vol. 37 Issue 1, p139
In this paper, we consider the number of zeros of Î”n f(z), Î”n f(z) - P(z) and Î”nf(z)/f(z) - P(z), where P(z) is a non-zero polynomial and f(z) is a transcendental meromorphic function of order Ï (f) â‰¤ 1, and corresponding exponents of convergence of these zeros are estimated...

- Fixed Points of Meromorphic Solutions for Some Difference Equations. Zong-Xuan Chen; Kwang Ho Shon // Abstract & Applied Analysis;2013, p1
We investigate fixed points of meromorphic solutions y(z) for the Pielou logistic equation and obtain some estimates of exponents of convergence of fixed points of y(z) and its shifts y(z+n), differences y(z) = y(z+1)/y(z), and divided differences y(z)/y(z).

- Growth of Meromorphic Solutions of Some q-Difference Equations. Guowei Zhang // Abstract & Applied Analysis;2013, p1
We estimate the growth of the meromorphic solutions of some complex q-difference equations and investigate the convergence exponents of fixed points and zeros of the transcendental solutions of the second order q-difference equation. We also obtain a theorem about the q-difference equation...

- Recent Trends in the Numerical Solution of Differential Equations: Preface. Brugnano, Luigi // AIP Conference Proceedings;9/15/2008, Vol. 1048 Issue 1, p861
The article discusses various reports published within the issue, including one on parallel approach in solving differential equations and another on high-order block methods.

- The Fixed Points of Solutions of Some q-Difference Equations. Xiu-Min Zheng; Hong-Yan Xu; Jun-Feng Xu // Abstract & Applied Analysis;2014, p1
The purpose of this paper is to investigate the fixed points of solutions f(z) of some q-difference equations and obtain some results about the exponents of convergence of fixed points of f(z) and f(qj z) (j âˆˆ â„•+), q-differences Î”q f(z) = f (qz) - f(z), and q-divided differences...