1. On some higher order equations admitting meromorphic solutions in a given domain
- Author
-
G. Barsegian and Fanning Meng
- 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 - 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.
- Published
- 2020