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 Pm t=0 ft (w ′)m−t = 0 are considered. Here the coefficients ft are functions of x, y, of u, v and the partial derivatives of u, v. Assuming that certain growth conditions for the coefficients ft are valid in the preimage under w of five distinct complex values, we find growth estimates, in the whole complex plane, for the order ρ(w) and the unintegrated Ahlfors-Shimizu characteristic A(r, w).