On meromorphic solutions of certain Fermat-type difference and analogues equations concerning open problems
Rajib Mandal, Raju Biswas, Sudip Kumar Guin
TL;DR
This paper investigates Fermat-type difference equations, demonstrating that their meromorphic solutions are generated by Riccati functions, and resolves open problems posed by Liu and Yang with supporting examples.
Contribution
It identifies the meromorphic solutions of certain Fermat-type difference equations as Riccati-generated and solves previously open problems in this area.
Findings
Meromorphic solutions are generated by Riccati functions.
Resolved open problems posed by Liu and Yang.
Provided examples to support the claims.
Abstract
In this paper, we have found that some certain Fermat-type shift and difference equations have the meromorphic solutions generated by Riccati type functions. Also we have solved the open problems posed by Liu and Yang (A note on meromorphic solutions of Fermat types equations, An. Stiint. Univ. Al. I. Cuza Lasi Mat. (N. S.), 62(2)(1), 317-325 (2016)). We have fortified the claims by some examples.
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Taxonomy
TopicsMeromorphic and Entire Functions · Advanced Differential Equations and Dynamical Systems