Titre : On the solutions of Fermat type quadratic trinomial equations in ℂ<sup>2</sup> generated by first order linear C-SHIFT and partial differential operators 

Auteurs : Abhijit Banerjee
, Jhuma Sarkar,  

Revue : Advances in Pure and Applied Mathematics 

Numéro : Issue 1 (January 2024) 

Volume : 15 

Date : 2024/01/5 

DOI : 10.21494/ISTE.OP.2023.1049 

ISSN : 1869-6090 

Résumé : This article is devoted to explore various forms of transcendental entire solution of different quadratic trinomials generated by first order linear c-shift operator. We also investigate the forms of solutions of certain quadratic trinomials under linear and mixed partial differential operators. Our paper improves the results of Li-Xu [Axioms, 126(10)(2021), 1-19] in two directions. In addition, in a corollary, deducted from one of our main result, we extend a result of Zhang et al. [ Aims Math., 7(2022), 11597-11613]. A series of examples have been exhibited to justify the existence and forms of transcendental entire solution of such equations. In the last section of the paper we have put a relevant question for future research. 

Éditeur : ISTE OpenScience