Zeros, poles, and fixed points of solution and its difference for some types of difference equations

Xu, Hong Yan; Zheng, Xiu Min

doi:10.1007/s10986-020-09503-8

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2022

2023

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“…Recently, there has been an increasing interest in the study on the properties of meromorphic solutions of complex difference equations from the viewpoint of difference analogues of Nevanlinna theory (see [4,6,8]) and among those many good results are obtained for the case of complex linear difference equations (see [4,5,6,11,12,14,16,19,20]). For the case of complex linear differential-difference equations see [1,2,3,13,15,21].…”

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confidence: 99%

Growth and value distribution of linear difference polynomials generated by meromorphic solutions of higher-order linear difference equations

Luo,

Zheng

2023

ejde

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In this article, we investigate the relationship between growth and value distribution of meromorphic solutions for the higher-order complex linear difference equations $$ A_n(z)f(z+n)+\dots+A_1(z)f(z+1)+A_0(z)f(z)=0 \quad \text{and } =F(z), $$ and for the linear difference polynomial $$ g(z)=\alpha_n(z)f(z+n)+\dots+\alpha_1(z)f(z+1)+\alpha_0(z)f(z) $$ generated by $f(z)$ where $A_j(z)$, $\alpha_j(z)$ ($j=0,1,\ldots,n$), $F(z)$ $(\not\equiv0)$ are meromorphic functions. We improve some previous results due to Belaidi, Chen and Zheng and others. For more information see https://ejde.math.txstate.edu/Volumes/2023/84/abstr.html

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