JournalszaaVol. 21, No. 2pp. 495–503

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
Stability Phenomenon for Generalizations of Algebraic Differential Equations cover
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Abstract

Certain stability properties for meromorphic solutions w(z)=u(x,y)+iv(x,y)w(z) = u(x,y) + i v(x,y) of partial differential equations of the form mt=0ft(w2)mt=0\sum^m–{t=0}f_t(w^2)^{m–t} = 0 are considered. Here the coefficients ftf_t are functions of x,yx, y, of u,vu,v and the partial derivatives of u,vu,v. Assuming that certain growth conditions for the coefficients ftf_t are valid in the preimage under ww of five distinct complex values, we find growth estimates, in the whole complex plane, for the order ρ(w)\rho (w) and the unintegrated Ahlfors-Shimizu characteristic A(r,w)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