On solutions of several Fermat-type partial differential-difference equations in C ²

In this paper, we study entire solutions of several Fermat-type partial differential-difference equations in <m:math xmlns:m="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <m:msup> <m:mrow> <m:mi mathvariant="double-struck">C</m:mi> </m:mrow> <m:mrow> <m:mn>2</m:mn> </m:mrow> </m:msup> </m:math> C² by applying Nevanlinna theory of meromorphic functions in several complex variables. We establish several theorems that characterize the forms of entire solutions for these equations. Our results extend and improve some previous results obtained by Xu and Cao [ Solutions of complex Fermat-type partial difference and differential-difference equations , Mediterr. J. Math. 15 (2018), 1–14] and Zheng and Xu [ Entire solutions for some Fermat type functional equations concerning difference and partial differential in <m:math xmlns:m="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <m:mi mathvariant="double-struck">C</m:mi> </m:math> C , Anal. Math. 48 (2022), 199–226].