Finite logarithmic order meromorphic solutions of linear difference/differential-difference equations
Abdelkader Dahmani, Benharrat Belaïdi
Received July 15, 2023. Published online June 5, 2024.
Abstract: Firstly we study the growth of meromorphic solutions of linear difference equation of the form
$A_k(z)f(z+c_k)+\cdots+A_1(z)f(z+c_1)+A_0(z)f(z)=F(z)$,
where $A_k(z),\ldots,A_0(z)$ and $F(z)$ are meromorphic functions of finite logarithmic order, $c_i$ $(i=1,\ldots,k, k\in\mathbb{N})$ are distinct nonzero complex constants. Secondly, we deal with the growth of solutions of differential-difference equation of the form
$\sum_{i=0}^n\sum_{j=0}^mA_{ij}(z)f^{(j)}(z+c_i)=F(z)$,
where $A_{ij}(z)$ $(i=0,1,\ldots,n, j=0,1,\ldots,m,n, m\in\mathbb{N})$ and $F(z)$ are meromorphic functions of finite logarithmic order, $c_i$ $(i=0,\ldots,n)$ are distinct complex constants. We extend some previous results obtained by Zhou and Zheng and Biswas to the logarithmic lower order.
Keywords: linear difference equation; linear differential-difference equation; meromorphic function; logarithmic order; logarithmic lower order
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Affiliations: Abdelkader Dahmani, Benharrat Belaïdi (corresponding author), Department of Mathematics, Laboratory of Pure and Applied Mathematics, University of Mostaganem (UMAB), B. P. 227 Mostaganem, Algeria, e-mail: abdelkader.dahmani.etu@univ-mosta.dz, benharrat.belaidi@univ-mosta.dz
