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ON UNICITY OF MEROMORPHIC SOLUTIONS TO DIFFERENCE EQUATIONS OF MALMQUIST TYPE

Part of: Difference equations Differential equations in the complex domain Difference and functional equations Entire and meromorphic functions, and related topics

Published online by Cambridge University Press:  05 August 2015

FENG LÜ ,
QI HAN  and
WEIRAN LÜ
FENG LÜ
Affiliation:
College of Science, China University of Petroleum, Qingdao, Shandong 266580, PR China email lvfeng18@gmail.com
QI HAN*
Affiliation:
Department of Mathematics, Worcester Polytechnic Institute, Worcester, MA 01609, USA email qhan@wpi.edu
WEIRAN LÜ
Affiliation:
College of Science, China University of Petroleum, Qingdao, Shandong 266580, PR China email uplvwr@yahoo.com.cn
*
✉qhan@wpi.edu
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Abstract

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In this note, we prove a uniqueness theorem for finite-order meromorphic solutions to a class of difference equations of Malmquist type. Such solutions $f$ are uniquely determined by their poles and the zeros of $f-e_{j}$ (counting multiplicities) for two finite complex numbers $e_{1}\neq e_{2}$.

Keywords

difference equationmeromorphic solutionNevanlinna theoryunicity

MSC classification

Primary: 30D35: Distribution of values, Nevanlinna theory
Secondary: 34M05: Entire and meromorphic solutions 39A10: Difference equations, additive 39B32: Equations for complex functions
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 93 , Issue 1 , February 2016 , pp. 92 - 98
Copyright
© 2015 Australian Mathematical Publishing Association Inc. 

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