Property of meromorphic solutions of certain nonlinear differential and difference equations

By applying Nevanlinna's value distribution theory of meromorphic functions, the following problems are investigated: the existence of finite order transcendental meromorphic solutions of several kinds nonlinear difference equations, and differential-difference equations of the form $~f^{n}(z)+M(z,f)=h(z)$, where n$(\geq3)$ is an integer, $h(z)$ is a given non-vanishing rational function, and $M(z,f)$ is a linear differential-difference polynomial with small meromorphic coefficients.