scholarly journals SOME NOVEL APPLICATIONS OF CERTAIN HIGHER ORDER ORDINARY COMPLEX DIFFERENTIAL EQUATIONS TO NORMALIZED ANALYTIC FUNCTIONS

2015 ◽  
Vol 5 (3) ◽  
pp. 479-484
Keyword(s):  
Differential Equations ◽  
Analytic Functions ◽  
Higher Order ◽  
Complex Differential Equations ◽  
Novel Applications

On some generalized Painlevé and Hayman type equations with meromorphic solutions in a bounded domain

2018 ◽  
Vol 25 (2) ◽  
pp. 187-194 ◽  
Author(s):  
Grigor Barsegian ◽  
Wenjun Yuan
Keyword(s):  
Differential Equations ◽  
Bounded Domain ◽  
Meromorphic Functions ◽  
Upper Bounds ◽  
Higher Order ◽  
Value Distribution ◽  
Meromorphic Solutions ◽  
Painleve Equations ◽  
Complex Differential Equations ◽  
Similar Solutions

Abstract The value distribution and, in particular, the numbers of a-points, have not been studied for meromorphic functions which are solutions of some complex differential equations in a given domain. Instead, the numbers of good a-points and Ahlfors islands, which play to a certain extend a role similar to that of the numbers of a-points, have been considered in some recent papers. In this paper, we consider meromorphic functions in a given domain, which are the solutions of some higher order equations and largely generalize the solutions of Painlevé equations 3–6. We give the upper bounds for the numbers of good a-points and Ahlfors islands of similar solutions.

scholarly journals Value Distribution of Meromorphic Solutions and Their Derivatives of Complex Differential Equations

2013 ◽  
Vol 2013 ◽  
pp. 1-5 ◽  
Author(s):  
Abdallah El Farissi
Keyword(s):  
Differential Equations ◽  
Meromorphic Functions ◽  
Higher Order ◽  
Value Distribution ◽  
Meromorphic Solutions ◽  
Small Functions ◽  
Complex Differential Equations ◽  
Linear Differential ◽  
The Relationship ◽  
Derivatives Of

We deal with the relationship between the small functions and the derivatives of solutions of higher-order linear differential equations f(k)+Ak-1f(k-1)+⋯+A0f=0,   k≥2, where Aj(z)  (j=0,1,…,k-1) are meromorphic functions. The theorems of this paper improve the previous results given by El Farissi, Belaïdi, Wang, Lu, Liu, and Zhang.

On some higher order equations admitting meromorphic solutions in a given domain

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Grigor Barsegian ◽  
Fanning Meng
Keyword(s):  
Differential Equations ◽  
Complex Plane ◽  
Recent Trend ◽  
Upper Bounds ◽  
Higher Order ◽  
General Nature ◽  
Meromorphic Solutions ◽  
Complex Differential Equations ◽  
Similar Solutions ◽  
Higher Order Differential Equations

AbstractThis 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.

Sign in / Sign up

Export Citation Format

Share Document