Difference analogue of the Lemma on the Logarithmic Derivative with applications to difference equations |
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Authors: | RG Halburd |
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Institution: | a Department of Mathematical Sciences, Loughborough University, Loughborough, Leicestershire, LE11 3TU, UK b Department Mathematics, University of Joensuu, PO Box 111, FI-80101 Joensuu, Finland |
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Abstract: | 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. |
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Keywords: | Logarithmic difference Nevanlinna theory Difference equation |
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