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Growth of meromorphic solutions of delay differential equations


Authors: Rod Halburd and Risto Korhonen
Journal: Proc. Amer. Math. Soc. 145 (2017), 2513-2526
MSC (2010): Primary 30D35; Secondary 34K40, 34M55
DOI: https://doi.org/10.1090/proc/13559
Published electronically: February 20, 2017
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Abstract: Necessary conditions are obtained for certain types of rational delay differential equations to admit a non-rational meromorphic solution of hyper-order less than one. The equations obtained include delay Painlevé equations and equations solved by elliptic functions.


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Additional Information

Rod Halburd
Affiliation: Department of Mathematics, University College London, Gower Street, London WC1E 6BT, United Kingdom
Email: r.halburd@ucl.ac.uk

Risto Korhonen
Affiliation: Department of Physics and Mathematics, University of Eastern Finland, P.O. Box 111, FI-80101 Joensuu, Finland
Email: risto.korhonen@uef.fi

DOI: https://doi.org/10.1090/proc/13559
Received by editor(s): February 26, 2016
Received by editor(s) in revised form: July 17, 2016
Published electronically: February 20, 2017
Additional Notes: The first author was partially supported by EPSRC grant EP/K041266/1
The second author was partially supported by the Academy of Finland grants (#286877) and (#268009)
Communicated by: Mourad Ismail
Article copyright: © Copyright 2017 American Mathematical Society