Abstract
In a recent paper [1], Ablowitz, Halburd and Herbst applied Nevanlinna theory to prove some results on complex difference equations reminiscent of the classical Malmquist theorem in complex differential equations. A typical example of their results tells us that if a complex difference equation y(z + 1) + y(z − 1) = R(z, y) with R(z, y) rational in both arguments admits a transcendental meromorphic solution of finite order, then degy R(z, y) ≤ 2. Improvements and extensions of such results are presented in this paper. In addition to order considerations, a result (see Theorem 13) is proved to indicate that solutions having Borel exceptional zeros and poles seem to appear in special situations only.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
