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Zeitschrift für Analysis und ihre Anwendungen


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Volume 21, Issue 2, 2002, pp. 495–503
DOI: 10.4171/ZAA/1089

Published online: 2002-06-30

Stability Phenomenon for Generalizations of Algebraic Differential Equations

G. Barsegian[1], Heinrich Begehr[2] and Ilpo Laine[3]

(1) National Acad. of Sciences, Yerevan, Armenia
(2) Freie Universität Berlin, Germany
(3) University of Joensuu, Finland

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 $A(r,w)$.

Keywords: Algebraic differential equations, growth of meromorphic functions, stability of growth

Barsegian G., Begehr Heinrich, Laine Ilpo: Stability Phenomenon for Generalizations of Algebraic Differential Equations. Z. Anal. Anwend. 21 (2002), 495-503. doi: 10.4171/ZAA/1089