Geodesic
The growth of solutions of algebraic differential equations
Atti della Accademia nazionale dei Lincei. Rendiconti Lincei. Matematica e applicazioni, Série 9, Tome 7 (1996) no. 2, pp. 67-73

Voir la notice de l'article provenant de la source Biblioteca Digitale Italiana di Matematica

Suppose that \( f(z) \) is a meromorphic or entire function satisfying \( P(z, f, f', \ldots , f^{(n)}) = 0 \) where \( P \) is a polynomial in all its arguments. Is there a limitation on the growth of \( f \), as measured by its characteristic \( T(r, f) \)? In general the answer to this question is not known. Theorems of Gol'dberg, Steinmetz and the author give a positive answer in certain cases. Some illustrative examples are also given. 
@article{RLIN_1996_9_7_2_a1,
     author = {Hayman, Walter K.},
     title = {The growth of solutions of algebraic differential equations},
     journal = {Atti della Accademia nazionale dei Lincei. Rendiconti Lincei. Matematica e applicazioni},
     pages = {67--73},
     publisher = {mathdoc},
     volume = {Ser. 9, 7},
     number = {2},
     year = {1996},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/RLIN_1996_9_7_2_a1/}
}
TY  - JOUR
AU  - Hayman, Walter K.
TI  - The growth of solutions of algebraic differential equations
JO  - Atti della Accademia nazionale dei Lincei. Rendiconti Lincei. Matematica e applicazioni
PY  - 1996
SP  - 67
EP  - 73
VL  - 7
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/RLIN_1996_9_7_2_a1/
LA  - en
ID  - RLIN_1996_9_7_2_a1
ER  - 
%0 Journal Article
%A Hayman, Walter K.
%T The growth of solutions of algebraic differential equations
%J Atti della Accademia nazionale dei Lincei. Rendiconti Lincei. Matematica e applicazioni
%D 1996
%P 67-73
%V 7
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/RLIN_1996_9_7_2_a1/
%G en
%F RLIN_1996_9_7_2_a1
Hayman, Walter K. The growth of solutions of algebraic differential equations. Atti della Accademia nazionale dei Lincei. Rendiconti Lincei. Matematica e applicazioni, Série 9, Tome 7 (1996) no. 2, pp. 67-73. http://geodesic.mathdoc.fr/item/RLIN_1996_9_7_2_a1/