Geodesic
On the order of growth of transcendental entire solutions of algebraic differential equations of second order
Sbornik. Mathematics, Tome 14 (1971) no. 2, pp. 281-296 
V. V. Zimoglyad. On the order of growth of transcendental entire solutions of algebraic differential equations of second order. Sbornik. Mathematics, Tome 14 (1971) no. 2, pp. 281-296. http://geodesic.mathdoc.fr/item/SM_1971_14_2_a7/
@article{SM_1971_14_2_a7,
     author = {V. V. Zimoglyad},
     title = {On the order of growth of transcendental entire solutions of algebraic differential equations of second order},
     journal = {Sbornik. Mathematics},
     pages = {281--296},
     year = {1971},
     volume = {14},
     number = {2},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1971_14_2_a7/}
}
TY  - JOUR
AU  - V. V. Zimoglyad
TI  - On the order of growth of transcendental entire solutions of algebraic differential equations of second order
JO  - Sbornik. Mathematics
PY  - 1971
SP  - 281
EP  - 296
VL  - 14
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/SM_1971_14_2_a7/
LA  - en
ID  - SM_1971_14_2_a7
ER  - 
%0 Journal Article
%A V. V. Zimoglyad
%T On the order of growth of transcendental entire solutions of algebraic differential equations of second order
%J Sbornik. Mathematics
%D 1971
%P 281-296
%V 14
%N 2
%U http://geodesic.mathdoc.fr/item/SM_1971_14_2_a7/
%G en
%F SM_1971_14_2_a7

Voir la notice de l'article provenant de la source Math-Net.Ru

The basic result is the following. Theorem. A differential equation of the form $P(z,y,y',y'')=0$, where $P(z,u,v,w)$ is a polynomial in the variables $z$, $u$, $v$ and $w$, cannot be satisfied by entire transcendental functions of zero order of growth. Figures: 1. Bibliography: 10 titles.

[1] G. Polya, “Zur Untersuchung der Grossenordnung ganzer Funktionen, die einer Differentialgleichung geniigen”, Acta Math., 42 (1920), 309–316 | DOI | MR

[2] G. Valiron, “Sur une fonction entiere d'ordre nul qui est solution d'une equation differentielle algebrique”, C. R. Acad. Sci., 180 (1925), 571–572 | Zbl

[3] G. Valiron, “Sur fonctions entieres d'ordre nul et les equations differentielles”, Bull. Soc. math. France, 53 (1925), 34–42 | MR | Zbl

[4] G. Valiron, “Fonctions analytiques et equations differentielles”, J. Math. Pures et Appl., 31 (1952), 293–303 | MR | Zbl

[5] Zh. Valiron, Analiticheskie funktsii, Gostekhizdat, Moskva, 1957

[6] B. Ya. Levin, Raspredelenie kornei tselykh funktsii, Gostekhizdat, Moskva, 1956

[7] I. V. Ostrovskii, “O tselykh funktsiyakh, udovletvoryayuschikh nekotorym spetsialnym neravenstvam”, Uchenye zapiski mekh.-mat. fak-ta i Kharkovskogo matem. ob-va, XXIX (1963), 145–168

[8] O. Blumenthal, “Sur le mode de croissonce des fonctions entieres”, Bull. Soc. Math. France, 35 (1907), 213–232 | MR | Zbl

[9] P. Nevanlinna, Uniformizatsiya, IL, Moskva, 1955

[10] A. J. Macintyre, “Wiman's method and the “flat regions” of integral functions”, Quart. J. Math., 9 (1938), 81–88 | DOI | Zbl