Abstract and Applied Analysis

On Growth of Meromorphic Solutions of Complex Functional Difference Equations

Jing Li, Jianjun Zhang, and Liangwen Liao

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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 α λ ( z ) ( ν = 1 n f ( z + c ν ) l λ , ν ) ) / ( μ J β μ ( z ) ( ν = 1 n f ( z + c ν ) m μ , ν ) ) = Q ( z , f ( p ( z ) ) ) , where I = { λ = ( l λ , 1 , l λ , 2 , , l λ , n ) l λ , ν { 0 } ,   ν = 1,2 , , n } and J = { μ = ( m μ , 1 , m μ , 2 , , m μ , n ) m μ , ν { 0 } ,   ν = 1,2 , , n } are two finite index sets, c ν ( ν = 1,2 , , n ) are distinct complex numbers, α λ ( z ) ( λ I ) and β μ ( 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 ) = p k z k + p k - 1 z k - 1 + + p 0 [ z ] of degree k 1 . We also give some examples to show that our results are sharp.

Article information

Source
Abstr. Appl. Anal., Volume 2014, Special Issue (2014), Article ID 828746, 6 pages.

Dates
First available in Project Euclid: 6 October 2014

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1412607234

Digital Object Identifier
doi:10.1155/2014/828746

Mathematical Reviews number (MathSciNet)
MR3176772

Zentralblatt MATH identifier
07023151

Citation

Li, Jing; Zhang, Jianjun; Liao, Liangwen. On Growth of Meromorphic Solutions of Complex Functional Difference Equations. Abstr. Appl. Anal. 2014, Special Issue (2014), Article ID 828746, 6 pages. doi:10.1155/2014/828746. https://projecteuclid.org/euclid.aaa/1412607234


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