Growth properties for solutions of differential equations defined in the disk
Let \(F\) be the class of meromorphic functions \(f\) in the unit disk \(D\) for which the Nevanlinna characteristic has a slow growth in the sense that \(\limsup_{r\to 1} T(r,f)/(-\log(1-r))=\alpha(f)<\infty\). This paper is devoted to consider the growth of solutions \(y_ 0\), such that \(\lim_{r\to 1} T(r,y_ 0)=+\infty\), of generalized algebraic differential equations of the form \(\sum_{\alpha\in I} f_ \alpha(z) y^{\alpha_ 0}(y')^{\alpha_ 1}\dots (y^{(k)})^{\alpha_ k}=0\) with coefficients \(f_ \alpha=f_{\alpha_ 0,\alpha_ 1,\dots, \alpha_ k}\) in the class \(F\). The results are too technical to be repeated here. Essentially, the idea is to find out additional assumptions which imply that \(y_ 0\in F\), too. For a related earlier paper, see \textit{S. Bank} [Ann. Mat. Pura Appl., IV. Ser. 92, 323-335 (1992; Zbl 0246.34004)].
scientific article; zbMATH DE number 169841