Difference analogue of the Lemma on the Logarithmic Derivative with applications to difference equations

The Lemma on the Logarithmic Derivative of a meromorphic function has many applications in the study of meromorphic functions and ordinary differential equations. In this paper, a difference analogue of the Logarithmic Derivative Lemma is presented and then applied to prove a number of results on me...

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Bibliographic Details
Published in:Journal of mathematical analysis and applications Vol. 314; no. 2; pp. 477 - 487
Main Authors: Halburd, R.G., Korhonen, R.J.
Format: Journal Article
Language:English
Published: San Diego, CA Elsevier Inc 15.02.2006
Elsevier
Subjects:
Difference equation
Exact sciences and technology
Finite differences and functional equations
Functions of a complex variable
Logarithmic difference
Mathematical analysis
Mathematics
Nevanlinna theory
Sciences and techniques of general use
Several complex variables and analytic spaces
Nevanlinna theory
Difference equation
Logarithmic difference
Mathematical analysis
Differential equation
Meromorphic function
ISSN:0022-247X, 1096-0813
Online Access:Get full text
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Summary:The Lemma on the Logarithmic Derivative of a meromorphic function has many applications in the study of meromorphic functions and ordinary differential equations. In this paper, a difference analogue of the Logarithmic Derivative Lemma is presented and then applied to prove a number of results on meromorphic solutions of complex difference equations. These results include a difference analogue of the Clunie lemma, as well as other results on the value distribution of solutions.
ISSN:0022-247X
1096-0813
DOI:10.1016/j.jmaa.2005.04.010