On Growth of Meromorphic Solutions for Linear Difference Equations

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.

Download Full-text

On the growth analysis of meromorphic solutions of finite ϕ-order of linear difference equations

Analysis ◽

10.1515/anly-2018-0065 ◽

2020 ◽

Vol 40 (4) ◽

pp. 193-202

Author(s):

Sanjib Kumar Datta ◽

Nityagopal Biswas

Keyword(s):

Difference Equation ◽

Complex Plane ◽

Difference Equations ◽

Growth Analysis ◽

Linear Difference Equation ◽

Higher Order ◽

Meromorphic Solutions ◽

Linear Difference Equations ◽

Unbounded Function ◽

Growth Properties

AbstractIn this paper, we investigate some growth properties of meromorphic solutions of higher-order linear difference equationA_{n}(z)f(z+n)+\dots+A_{1}(z)f(z+1)+A_{0}(z)f(z)=0,where {A_{n}(z),\dots,A_{0}(z)} are meromorphic coefficients of finite φ-order in the complex plane where φ is a non-decreasing unbounded function. We extend some earlier results of Latreuch and Belaidi [Z. Latreuch and B. Belaïdi, Growth and oscillation of meromorphic solutions of linear difference equations, Mat. Vesnik 66 2014, 2, 213–222].

Download Full-text

On Meromorphic Solutions of Non-linear Difference Equations

Computational Methods and Function Theory ◽

10.1007/s40315-017-0223-1 ◽

2017 ◽

Vol 18 (3) ◽

pp. 389-408 ◽

Cited By ~ 2

Author(s):

Ran-Ran Zhang ◽

Zhi-Bo Huang

Keyword(s):

Difference Equations ◽

Meromorphic Solutions ◽

Linear Difference Equations ◽

Non Linear

Download Full-text

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

Symmetry ◽

10.3390/sym13020267 ◽

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.

Download Full-text