On the growth of meromorphic solutions of some algebraic differential equations
Let X, Y, a, \(a_{ij}\) be meromorphic functions satisfying \[ X^ n=aY^ m+\sum^{k}_{\nu =0}\sum_{i+j=\nu}a_{ij}X^ iY^ j,\quad XY\neq 0 \] and \(X^ n\neq aY^ m\). If \(n\geq m>k+2+m/n\), then \(T(r,X)=O(\sum T(r,a_{ij})+T(r,a))+S(r,X),\) \(r\to \infty\). This theorem has interesting applications to the meromorphic solutions of the differential equation \[ (w^{(m)})^ n+Q_{n-1}(w,z)(w^{(m)})^{n- 1}+...+Q_ 0(w,z)=0 \] with meromorphic coefficients.
scientific article; zbMATH DE number 4021621