Existence of Meromorphic Solutions of Fermat-Type Functional Equations

The functional equation f（z）~n+g（z）~n=1 can be interpreted as the Fermat-type equations over function field. In this paper, by using Nevanlinna theory of meromorphic functions, we investigate the existence of meromorphic solutions of hyper-order strictly less than 1 to the Fermat-type functional equation(a0f（z）+a1f（z+c）)3+(b0f（z）+b1f（z+c）)3= eαz+β,where a0, a1, b0, b1, α, β, c are complex constants and c≠0.