Abstract
The main purpose of this paper is to present the properties of the meromorphic solutions of complex difference equations of the form , where is a collection of all subsets of , are distinct, nonzero complex numbers, is a transcendental meromorphic function, 's are small functions relative to , and is a rational function in with coefficients which are small functions relative to .
Highlights
We assume that the readers are familiar with the basic notations of Nevanlinna’s value distribution theory; see 1–3
Recent interest in the problem of integrability of difference equations is a consequence of the enormous activity on Painlevedifferential equations and their discrete counterparts during the last decades
It is obvious that the left-hand side of 2.1 is just a product only
Summary
We assume that the readers are familiar with the basic notations of Nevanlinna’s value distribution theory; see 1–3 .Recent interest in the problem of integrability of difference equations is a consequence of the enormous activity on Painlevedifferential equations and their discrete counterparts during the last decades. If a complex difference equation f z 1 f z − 1 R z, f z a0 z b0 z a1 z f z b1 z f z ap bq zzffzzpq, 1.1 with rational coefficients ai z i 0, 1, . Q admits a transcendental meromorphic solution of finite order, degf R z, f z ≤ 2.
Sign-in/Register to view highlights & summary 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.
