ON THE ORDER OF GROWTH OF TRANSCENDENTAL ENTIRE SOLUTIONS OF ALGEBRAIC DIFFERENTIAL EQUATIONS OF SECOND ORDER

1971 ◽  
Vol 14 (2) ◽  
pp. 281-296
Author(s):  
V V Zimogljad
Keyword(s):  
Differential Equations ◽  
Second Order ◽  
Order Of Growth ◽  
Entire Solutions ◽  
Algebraic Differential Equations

scholarly journals Order of growth of solutions to algebraic differential equations in the unit disk

2004 ◽  
Vol 2004 (41) ◽  
pp. 2161-2170 ◽  
Author(s):  
D. Benbourenane ◽  
L. R. Sons
Keyword(s):  
Differential Equations ◽  
Unit Disk ◽  
Finite Order ◽  
Meromorphic Solutions ◽  
Order Of Growth ◽  
Growth Estimate ◽  
Algebraic Differential Equations ◽  
Uniform Growth ◽  
Growth Of Solutions

S. B. Bank has shown that there is no uniform growth estimate for meromorphic solutions of algebraic differential equations with meromorphic coefficients in the unit disk. We give conditions under which such solutions must have a finite order of growth.

On the hypertranscendence of meromorphic solutions of certain functional equations

1979 ◽  
Vol 83 (1-2) ◽  
pp. 45-54 ◽  
Author(s):  
Steven B. Bank
Keyword(s):  
Differential Equations ◽  
Functional Equations ◽  
Meromorphic Solutions ◽  
Entire Solutions ◽  
Algebraic Differential Equations

SynopsisThis paper deals mainly with showing that meromorphic solutions of Poincaré functional equations cannot satisfy algebraic differential equations. Results of this type for entire solutions have previously been obtained by H. Wittich.

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