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 On some special difference equations of Malmquist type Bull. Korean Math. Soc. 2018 Vol. 55, No. 1, 51-61 https://doi.org/10.4134/BKMS.b160844Published online January 31, 2018 Jie Zhang China University of Mining and Technology Abstract : 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 Downloads: Full-text PDF