On Growth of Meromorphic Solutions of Complex Functional Difference Equations

Jing Li, Jianjun Zhang and Liangwen Liao

Abstract and Applied Analysis, 2014, vol. 2014, issue 1

Abstract: The main purpose of this paper is to investigate the growth order of the meromorphic solutions of complex functional difference equation of the form (∑λ∈I αλ(z)(∏ν=1n f(z+cν) lλ,ν))/(∑μ∈J βμ(z)(∏ν=1n f(z+cν) mμ,ν))=Q(z, f(p(z))), where I = {λ = (lλ,1, lλ,2, …, lλ,n)∣lλ,ν ∈ ℕ⋃ {0}, ν = 1,2, …, n} and J = {μ = (mμ,1, mμ,2, …, mμ,n)∣mμ,ν ∈ ℕ⋃ {0}, ν = 1,2, …, n} are two finite index sets, cν (ν = 1,2, …, n) are distinct complex numbers, αλ(z) (λ ∈ I) and βμ(z) (μ ∈ J) are small functions relative to f(z), and Q(z, u) is a rational function in u with coefficients which are small functions of f(z), p(z) = pkzk + pk−1zk−1 + ⋯+p0 ∈ ℂ[z] of degree k ≥ 1. We also give some examples to show that our results are sharp.

Date: 2014
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https://doi.org/10.1155/2014/828746

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Persistent link: https://EconPapers.repec.org/RePEc:wly:jnlaaa:v:2014:y:2014:i:1:n:828746

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