On generalized Fermat Diophantine functional and partial differential equations in C2

In this paper, we characterize meromorphic solutions f (z(1), z(2)), g (z(1), z(2)) to the generalized Fermat Diophantine functional equations h(z(1), z(2)) f(m) + k(z(1), z(2))g(n) = 1 in C-2 for integers m, n >= 2 and nonzero meromorphic functions h(z(1), z(2)), k (z(1), z(2)) in C-2. Meromorphic solutions to associated partial differential equations are also studied.