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On some higher order equations admitting meromorphic solutions in a given domain
- Source :
- Georgian Mathematical Journal. 28:529-532
- Publication Year :
- 2020
- Publisher :
- Walter de Gruyter GmbH, 2020.
-
Abstract
- This paper relates to a recent trend in complex differential equations which studies solutions in a given domain. The classical settings in complex equations were widely studied for meromorphic solutions in the complex plane. For functions in the complex plane, we have a lot of results of general nature, in particular, the classical value distributions theory describing numbers of a-points. Many of these results do not work for functions in a given domain. A recent principle of derivatives permits us to study the numbers of Ahlfors simple islands for functions in a given domain; the islands play, to some extend, a role similar to that of the numbers of simple a-points. In this paper, we consider a large class of higher order differential equations admitting meromorphic solutions in a given domain. Applying the principle of derivatives, we get the upper bounds for the numbers of Ahlfors simple islands of similar solutions.
- Subjects :
- Work (thermodynamics)
Pure mathematics
Higher order equations
Complex differential equation
General Mathematics
010102 general mathematics
01 natural sciences
Domain (mathematical analysis)
010101 applied mathematics
Simple (abstract algebra)
0101 mathematics
Value (mathematics)
Complex plane
Mathematics
Meromorphic function
Subjects
Details
- ISSN :
- 15729176 and 1072947X
- Volume :
- 28
- Database :
- OpenAIRE
- Journal :
- Georgian Mathematical Journal
- Accession number :
- edsair.doi...........ea577bc5c63f41efa00d5465de7fdc9c