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

2015 ◽  
Vol 5 (3) ◽  
pp. 479-484
2018 ◽  
Vol 25 (2) ◽  
pp. 187-194 ◽  
Author(s):  
Grigor Barsegian ◽  
Wenjun Yuan

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.


2013 ◽  
Vol 2013 ◽  
pp. 1-5 ◽  
Author(s):  
Abdallah El Farissi

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.


2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Grigor Barsegian ◽  
Fanning Meng

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.


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