Bulletin of the
Korean Mathematical Society BKMS

In this article, we mainly use Nevanlinna theory to investigate some special difference equations of malmquist type such as $f^2+{(\Delta_c f)}^2={\beta}^2$, ${f}^2+{(\Delta_cf)}^2=R$, ${f'}^2+{(\Delta_cf)}^2=R$ and $f^2+{\big(f(z+c)\big)}^2=R$, where $\beta$ is a nonzero small function of $f$ and $R$ is a nonzero rational function respectively. These discussions extend one related result due to C.~C.~Yang et al.~in some sense.

Keywords: Nevanlinna theory, uniqueness, difference equation, differential equation

MSC numbers: Primary 30D35, 30D05, 34M10