We obtain a Clunie type theorem for a rather general form of functional equations involving differential polynomials. Our theorems can give a much sharper estimate on the error term of the proximity function of solutions of differential equations and functional equations than the upper bound obtained by Clunie, Doeringer, He-Xiao, Korhonen and etc. In particular, our theorem can also be applied to study various types of Painlevé differential equations.
"Estimates of the proximate function of differential polynomials." Proc. Japan Acad. Ser. A Math. Sci. 83 (4) 50 - 55, April 2007. https://doi.org/10.3792/pjaa.83.50