Abstract and Applied Analysis

Some Properties on Complex Functional Difference Equations

Zhi-Bo Huang and Ran-Ran Zhang

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Abstract

We obtain some results on the transcendental meromorphic solutions of complex functional difference equations of the form λ I α λ ( z ) ( j = 0 n f ( z + c j ) λ j ) = R ( z , f p ) = ( ( a 0 ( z ) + a 1 ( z ) ( f p ) +   + a s ( z ) ( f p ) s ) / ( b 0 ( z ) + b 1 ( z ) ( f p ) +   + b t ( z ) ( f p ) t ) ) , where I is a finite set of multi-indexes λ = ( λ 0 , λ 1 , , λ n ) , c 0 = 0 , c j { 0 } ( j = 1,2 , , n ) are distinct complex constants, p ( z ) is a polynomial, and α λ ( z )    ( λ I ) , a i ( z )    ( i = 0,1 , , s ) , and b j ( z )    ( j = 0,1 , , t ) are small meromorphic functions relative to f ( z ) . We further investigate the above functional difference equation which has special type if its solution has Borel exceptional zero and pole.

Article information

Source
Abstr. Appl. Anal., Volume 2014, Special Issue (2014), Article ID 283895, 10 pages.

Dates
First available in Project Euclid: 6 October 2014

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1412607223

Digital Object Identifier
doi:10.1155/2014/283895

Mathematical Reviews number (MathSciNet)
MR3200774

Zentralblatt MATH identifier
07022088

Citation

Huang, Zhi-Bo; Zhang, Ran-Ran. Some Properties on Complex Functional Difference Equations. Abstr. Appl. Anal. 2014, Special Issue (2014), Article ID 283895, 10 pages. doi:10.1155/2014/283895. https://projecteuclid.org/euclid.aaa/1412607223


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