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Applications of Nevanlinna theory to q-difference equations

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thesis
posted on 15.08.2018, 08:18 by David C. Barnett
Recently Nevanlinna theory (the theory of meromorphic functions) has been used as a detector of integrability of difference equations. In this thesis we study meromorphic solutions of so-called q-difference equations and extend some key results from Nevanlinna theory to the q-difference operator. 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 thesis, a q-difference analogue of the Logarithmic Derivative Lemma is presented, and then applied to prove a number of results on meromorphic solutions of complex q-difference equations. These results include a difference analogue of the Clunie Lemma, as well as other results on the value distribution of solutions.

Funding

Engineering and Physical Sciences Research Council.

History

School

  • Science

Department

  • Mathematical Sciences

Publisher

© David Barnett

Publisher statement

This work is made available according to the conditions of the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0) licence. Full details of this licence are available at: https://creativecommons.org/licenses/by-nc-nd/4.0/

Publication date

2006

Notes

A Master's Thesis. Submitted in partial fulfilment of the requirements for the award of Master of Philosophy at Loughborough University.

Language

en

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