Meromorphic solutions of Fermat type differential and difference equations of certain types

In this paper, we mainly consider the Fermat type differential equation f (z)n + f & PRIME;(z)n = & phi;(z), where & phi;(z) = eh(z) or 1 - e2h(z), and h(z) is any entire function, and the Fermat type difference equation f (z)n + f (z + c)m = eP (z), where P (z) is any entire function and c is a non-zero constant. We also provide short proofs for some existence results without complicated computations using elliptic functions.

Automated summary

In this paper, we discuss the existence of solutions for Fermat type differential equations and Fermat type difference equations, and provide concise proofs using elliptic functions.