# Stability Phenomenon for Generalizations of Algebraic Differential Equations

### G. Barsegian

National Acad. of Sciences, Yerevan, Armenia### Heinrich Begehr

Freie Universität Berlin, Germany### Ilpo Laine

University of Joensuu, Finland

## Abstract

Certain stability properties for meromorphic solutions $w(z) = u(x,y) + i v(x,y)$ of partial differential equations of the form $\sum^m–{t=0}f_t(w^2)^{m–t} = 0$ 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 $A(r,w)$.

## Cite this article

G. Barsegian, Heinrich Begehr, Ilpo Laine, Stability Phenomenon for Generalizations of Algebraic Differential Equations. Z. Anal. Anwend. 21 (2002), no. 2, pp. 495–503

DOI 10.4171/ZAA/1089