Xu, HongyanXu, LingSrivastava, H.M.2022-11-122022-11-1220222022Xu, H., Xu, L., & Srivastava, H. M. (2022). “The exact solutions for several partial differential-difference equations with constant coefficients.” Mathematics, 10(19), 3596. https://doi.org/10.3390/math10193596https://doi.org/10.3390/math10193596http://hdl.handle.net/1828/14419This article is concerned with the description of the entire solutions of several Fermat type partial differential-difference equations (PDDEs) [μf(z) + λfz1(z)]^2 + [αf(z + c) - βf(z)]^2 = 1 and [μf(z) + λ1fz1(z) + λ2fz2(z)]^2 + [αf(z + c) - βf(z)]^2 = 1, where fz1(z) = ∂f/∂z1 and fz2(z) = ∂f/∂z2, c = (c1,c2) ∈ ℂ^2, α,β,μ,λ,λ1,λ2,c1,c2 are constants in ℂ. Our theorems in this paper give some descriptions of the forms of transcendental entire solutions for the above equations, which are some extensions and improvement of the previous theorems given by Xu, Cao, Liu, and Yang. In particular, we exhibit a series of examples to explain that the existence conditions and the forms of transcendental entire solutions with a finite order of such equations are precise.enNevanlinna theoryentire solutionpartial differential-difference equationArticleDepartment of Mathematics and Statistics