Transcendental entire solutions of several complex product-type nonlinear partial differential equations in ℂ2

Our purpose in this article is to describe the solutions of several product-type nonlinear partial differential equations (PDEs) and where is a nonconstant polynomial and , and are constants in . The finite-order transcendental entire solution of the first equation is of the following forms: or where , , and The description of the forms of the solutions for these PDEs demonstrates that our results are some improvements of the previous results given by Liu, Cao, and Xu [L. Xu and T. B. Cao, Solutions of complex Fermat-type partial difference and differential-difference equations, Mediterr. J. Math. (2018), 227], and [K. Liu and T. B. Cao, Entire solutions of Fermat type difference differential equations, Electron. J. Diff. Equ. (2013), No. 59, 1–10.]. Meantime, we list some examples to explain that the forms of solutions of our theorems are precise to some extent.