Stability phenomenon for generalizations of algebraic differential equations

Certain stability properties for meromorphic solutions w(z) = u(x, y) + i v(x, y) of partial differential equations of the form Sigma(t=0)(m) 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).