scholarly journals Value distribution of meromorphic solutions of homogeneous and non-homogeneous complex linear differential-difference equations

2016 ◽  
Vol 14 (1) ◽  
pp. 970-976 ◽  
Author(s):  
Li-Qin Luo ◽  
Xiu-Min Zheng
Keyword(s):  
Difference Equations ◽  
Value Distribution ◽  
Small Function ◽  
Meromorphic Solutions ◽  
Homogeneous Complex ◽  
Complex Linear ◽  
Linear Differential

AbstractIn this paper, we investigate the value distribution of meromorphic solutions of homogeneous and non-homogeneous complex linear differential-difference equations, and obtain the results on the relations between the order of the solutions and the convergence exponents of the zeros, poles, a-points and small function value points of the solutions, which show the relations in the case of non-homogeneous equations are sharper than the ones in the case of homogeneous equations.

scholarly journals Value Distribution and Arbitrary-Order Derivatives of Meromorphic Solutions of Complex Linear Differential Equations in the Unit Disc

Mathematics ◽  
2019 ◽  
Vol 7 (4) ◽  
pp. 352
Author(s):  
Hai-Ying Chen ◽  
Xiu-Min Zheng
Keyword(s):  
Differential Equation ◽  
Unit Disc ◽  
Arbitrary Order ◽  
Value Distribution ◽  
Small Function ◽  
Meromorphic Solutions ◽  
Exponent Of Convergence ◽  
Complex Linear ◽  
Linear Differential ◽  
Derivatives Of

In this paper, we investigate the value distribution of meromorphic solutions and their arbitrary-order derivatives of the complex linear differential equation f ′ ′ + A ( z ) f ′ + B ( z ) f = F ( z ) in Δ with analytic or meromorphic coefficients of finite iterated p-order, and obtain some results on the estimates of the iterated exponent of convergence of meromorphic solutions and their arbitrary-order derivatives taking small function values.

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.

scholarly journals Value Distribution of Meromorphic Solutions and Their Derivatives of Complex Differential Equations

2013 ◽  
Vol 2013 ◽  
pp. 1-5 ◽  
Author(s):  
Abdallah El Farissi
Keyword(s):  
Differential Equations ◽  
Meromorphic Functions ◽  
Higher Order ◽  
Value Distribution ◽  
Meromorphic Solutions ◽  
Small Functions ◽  
Complex Differential Equations ◽  
Linear Differential ◽  
The Relationship ◽  
Derivatives Of

We deal with the relationship between the small functions and the derivatives of solutions of higher-order linear differential equations f(k)+Ak-1f(k-1)+⋯+A0f=0,   k≥2, where Aj(z)  (j=0,1,…,k-1) are meromorphic functions. The theorems of this paper improve the previous results given by El Farissi, Belaïdi, Wang, Lu, Liu, and Zhang.

scholarly journals On q-Difference Riccati Equations and Second-Order Linear q-Difference Equations

2013 ◽  
Vol 2013 ◽  
pp. 1-10
Author(s):  
Zhi-Bo Huang
Keyword(s):  
Complex Plane ◽  
Difference Equations ◽  
Gamma Function ◽  
Riccati Equations ◽  
Second Order ◽  
Value Distribution ◽  
Meromorphic Solutions ◽  
Order Linear ◽  
Basic Properties ◽  
Casorati Determinant

We consider q-difference Riccati equations and second-order linear q-difference equations in the complex plane. We present some basic properties, such as the transformations between these two equations, the representations and the value distribution of meromorphic solutions of q-difference Riccati equations, and the q-Casorati determinant of meromorphic solutions of second-order linear q-difference equations. In particular, we find that the meromorphic solutions of these two equations are concerned with the q-Gamma function when q∈ℂ such that 0<|q|<1. Some examples are also listed to illustrate our results.

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 Consistent systems of linear differential and difference equations

2019 ◽  
Vol 21 (9) ◽  
pp. 2751-2792
Author(s):  
Reinhard Schäfke ◽  
Michael Singer
Keyword(s):  
Difference Equations ◽  
Linear Differential
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