scholarly journals Dual exponential polynomials and a problem of Ozawa

2021 ◽  
pp. 1-19
Author(s):  
Janne Heittokangas ◽  
Katsuya Ishizaki ◽  
Kazuya Tohge ◽  
Zhi-Tao Wen
Keyword(s):  
Differential Equations ◽  
Polynomial Solution ◽  
Linear Differential Equations ◽  
The Other ◽  
Exponential Polynomial ◽  
Exponential Polynomials ◽  
Open Problems ◽  
Duality Property ◽  
Complex Linear ◽  
Linear Differential

Complex linear differential equations with entire coefficients are studied in the situation where one of the coefficients is an exponential polynomial and dominates the growth of all the other coefficients. If such an equation has an exponential polynomial solution $f$ , then the order of $f$ and of the dominant coefficient are equal, and the two functions possess a certain duality property. The results presented in this paper improve earlier results by some of the present authors, and the paper adjoins with two open problems.

scholarly journals On [p,q]-order of growth of solutions of complex linear differential equations near a singular point

Filomat ◽  
2019 ◽  
Vol 33 (13) ◽  
pp. 4013-4020
Author(s):  
Jianren Long ◽  
Sangui Zeng
Keyword(s):  
Differential Equation ◽  
Singular Point ◽  
Differential Equations ◽  
Linear Differential Equation ◽  
Linear Differential Equations ◽  
Order Of Growth ◽  
Complex Linear ◽  
Linear Differential ◽  
Growth Of Solutions

We investigate the [p,q]-order of growth of solutions of the following complex linear differential equation f(k)+Ak-1(z) f(k-1) + ...+ A1(z) f? + A0(z) f = 0, where Aj(z) are analytic in C? - {z0}, z0 ? C. Some estimations of [p,q]-order of growth of solutions of the equation are obtained, which is generalization of previous results from Fettouch-Hamouda.

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