Stability phenomenon for generalizations of algebraic differential equations (Q699322)

Summary: Certain stability properties for meromorphic solutions \(w(z)=u(x,y) +iv(x,y)\) of partial differential equations of the form \(\sum^m_{t=0} f_t(w')^{m-t}=0\) are considered. Here the coefficients \(f_t\) are functions of \(x,y\), of \(u,v\) and the partial derivatives of \(u,v\). Assuming that certain growth conditions for the coefficients \(f_t\) are valid in the preimage under \(w\) of five distinct complex values, we find growth estimates, in the whole complex plane, for the order \(\rho(w)\) and the unintegrated Ahlfors-Shimizu characteristic \(A(r,w)\).