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 2006-02, Vol.314 (2), p.477-487
Main Authors: Halburd, R.G., Korhonen, R.J.
Format: Article
Language:English
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
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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