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Keywords:
linear difference equation; linear differential-difference equation; meromorphic function; logarithmic order; logarithmic lower order
linear difference equation; linear differential-difference equation; meromorphic function; logarithmic order; logarithmic lower order
Summary:
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 $$ \sum _{i=0}^{n}\sum _{j=0}^{m}A_{ij}(z)f^{(j)}(z+c_{i})=F(z), $$ 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.\looseness -1
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