Entire solutions for quadratic trinomial partial differential-difference functional equations in $\mathbb{C}^n$


Raju Biswas, Rajib Mandal




In this paper, we solve four certain quadratic trinomial partial differential-difference equations for finite order entire functions in $\mathbb{C}^n$. Our results significantly improve some earlier results, mainly the results due to Haldar and Ahamed (Entire solutions of several quadratic binomial and trinomial partial differential-difference equations in $\mathbb{C}^2$. Anal. Math. Physics 12(113) (2022)). The earlier results were on $\mathbb{C}^2$ whereas our results are on $\mathbb{C}^n$. We exhibit some examples to fortify our results.