On generalized Fermat Diophantine functional and partial differential equations in C2
Abstract
In this paper, we characterize meromorphic solutions f(z1,z2),g(z1,z2) to the generalized Fermat Diophantine functional equations h(z1,z2)fm+k(z1,z2)gn=1 in C2 for integers m,n≥2 and nonzero meromorphic functions h(z1,z2),k(z1,z2) in C2. Meromorphic solutions to associated partial differential equations are also studied.
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