Hayman, Walter K.. "The growth of solutions of algebraic differential equations." Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni 7.2 (1996): 67-73. <http://eudml.org/doc/244183>.
@article{Hayman1996,
abstract = {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.},
author = {Hayman, Walter K.},
journal = {Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni},
keywords = {Differential equations; Entire; Meromorphic; Growth; order of meromorphic function; meromorphic solution; Nevanlinna characteristic function},
language = {eng},
month = {10},
number = {2},
pages = {67-73},
publisher = {Accademia Nazionale dei Lincei},
title = {The growth of solutions of algebraic differential equations},
url = {http://eudml.org/doc/244183},
volume = {7},
year = {1996},
}
TY - JOUR
AU - Hayman, Walter K.
TI - The growth of solutions of algebraic differential equations
JO - Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni
DA - 1996/10//
PB - Accademia Nazionale dei Lincei
VL - 7
IS - 2
SP - 67
EP - 73
AB - 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.
LA - eng
KW - Differential equations; Entire; Meromorphic; Growth; order of meromorphic function; meromorphic solution; Nevanlinna characteristic function
UR - http://eudml.org/doc/244183
ER -