When an entire function and its linear differential polynomial share two values

Authors
Li, P Yang, CC
Citation
P. Li et Cc. Yang, When an entire function and its linear differential polynomial share two values, ILL J MATH, 44(2), 2000, pp. 349-362
Citations number
16
Categorie Soggetti
Mathematics
Journal title
ILLINOIS JOURNAL OF MATHEMATICS
ISSN journal
00192082 → ACNP
Volume
44
Issue
2
Year of publication
2000
Pages
349 - 362
Database
ISI
SICI code
0019-2082(200022)44:2<349:WAEFAI>2.0.ZU;2-R
Abstract
In this note, the relationship between a non-constant entire function f and its linear differential polynomial L(f) has been obtained when they share two finite values, ignoring multiplicities, by applying value distribution theory,. This confirms Frank's conjecture as a special case. Entire solutio ns of certain types of non-linear differential equations are also discussed .