Growth of meromorphic solutions of linear difference equations without dominating coefficients

Wei, Dong-Mei; Huang, Zhicheng

doi:10.1186/s13660-019-2065-z

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2021

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“…where A 1 (z) and A 0 (z) are entire functions of finite order. Under some restrictions on the coefficients, they gave an answer to the posed question, see also the papers [11,18]. So, it is interesting further research in this direction.…”

Section: Discussionmentioning

confidence: 97%

Study of the growth properties of meromorphic solutions of higher-order linear difference equations

Belaïdi

Bellaama

2021

Arab. J. Math.

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In this paper, we investigate the growth of meromorphic solutions of homogeneous and non-homogeneous linear difference equations $$\begin{aligned} A_{k}(z)f(z+c_{k})+\cdots +A_{1}(z)f(z+c_{1})+A_{0}(z)f(z)= & {} 0, \\ A_{k}(z)f(z+c_{k})+\cdots +A_{1}(z)f(z+c_{1})+A_{0}(z)f(z)= & {} F, \end{aligned}$$ A k ( z ) f ( z + c k ) + ⋯ + A 1 ( z ) f ( z + c 1 ) + A 0 ( z ) f ( z ) = 0 , A k ( z ) f ( z + c k ) + ⋯ + A 1 ( z ) f ( z + c 1 ) + A 0 ( z ) f ( z ) = F , where $$A_{k}\left( z\right) ,\ldots ,A_{0}\left( z\right) ,$$ A k z , … , A 0 z , $$F\left( z\right) $$ F z are meromorphic functions and $$c_{j}$$ c j $$\left( 1,\ldots ,k\right) $$ 1 , … , k are non-zero distinct complex numbers. Under some conditions on the coefficients, we extend early results due to Zhou and Zheng, Belaïdi and Benkarouba.

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Section: Discussionmentioning

confidence: 97%