On the growth analysis of meromorphic solutions of finite logarithmic order of linear difference equations in the unit disc

2021 ◽  
Author(s):  
Iqbal H. Jebril ◽  
Nityagopal Biswas ◽  
Sanjib Kumar Datta
Keyword(s):  
Difference Equations ◽  
Unit Disc ◽  
Growth Analysis ◽  
Meromorphic Solutions ◽  
Linear Difference Equations ◽  
Logarithmic Order

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

Analysis ◽  
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].

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

Symmetry ◽  
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.

scholarly journals Growth of Meromorphic Solutions of Finite Logarithmic Order of Linear Difference Equations

2015 ◽  
Vol 54 (1) ◽  
pp. 5-20
Author(s):  
Benharrat Belaïdi
Keyword(s):  
Difference Equation ◽  
Difference Equations ◽  
Meromorphic Functions ◽  
Linear Difference Equation ◽  
Meromorphic Solutions ◽  
Linear Difference Equations ◽  
Logarithmic Order ◽  
Oscillation Of Solutions

Abstract In this paper, we deal with the growth and the oscillation of solutions of the linear difference equation an (z) f (z + n) + an-1 (z) f (z + n - 1) + ··· + a1 (z) f (z + 1) + a0 (z) f (z) = 0; where an(z),···, a0(z) are meromorphic functions of finite logarithmic order such that an(z)a0(z) 6≢ 0.

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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