Uniqueness for meromorphic solutions of Schwarzian differential equation

Abstract

<abstract><p>Let $ f $ be a meromorphic function, $ R $ be a nonconstant rational function and $ k $ be a positive integer. In this paper, we consider the Schwarzian differential equation of the form</p> <p><disp-formula> <label/> <tex-math id="FE1"> \begin{document}$ \begin{align*} \left[\frac{f'''}{f'}-\frac{3}{2}\left(\frac{f''}{f'}\right)^{2}\right]^{k} = R(z). \end{align*} $\end{document} </tex-math></disp-formula></p> <p>We investigate the uniqueness of meromorphic solutions of the above Schwarzian differential equation if the meromorphic solution $ f $ shares three values with any other meromorphic function.</p></abstract>