scholarly journals Some Oscillation Results of Higher-Order Linear Differential Equations with Meromorphic Coefficients

2012 ◽  
Vol 2012 ◽  
pp. 1-11
Author(s):  
Zhigang Huang
Keyword(s):  
Differential Equations ◽  
Higher Order ◽  
Linear Differential Equations ◽  
Order Linear ◽  
Small Functions ◽  
Linear Differential ◽  
The Relationship ◽  
Growth Of Solutions

We investigate the growth of solutions of higher-order nonhomogeneous linear differential equations with meromorphic coefficients. We also discuss the relationship between small functions and solutions of such equations.

scholarly journals Relation between Small Functions with Differential Polynomials Generated by Solutions of Linear Differential Equations

2012 ◽  
Vol 2012 ◽  
pp. 1-11
Author(s):  
Zhigang Huang
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Linear Differential Equation ◽  
Entire Functions ◽  
Linear Differential Equations ◽  
Differential Polynomials ◽  
Small Functions ◽  
Linear Differential ◽  
The Relationship ◽  
Growth Of Solutions

This paper is devoted to studying the growth of solutions of second-order nonhomogeneous linear differential equation with meromorphic coefficients. We also discuss the relationship between small functions and differential polynomialsL(f)=d2f″+d1f′+d0fgenerated by solutions of the above equation, whered0(z),d1(z),andd2(z)are entire functions that are not all equal to zero.

scholarly journals Complex Oscillation of Higher-Order Linear Differential Equations with Coefficients Being Lacunary Series of Finite Iterated Order

2013 ◽  
Vol 2013 ◽  
pp. 1-8
Author(s):  
Jin Tu ◽  
Hong-Yan Xu ◽  
Hua-ming Liu ◽  
Yong Liu
Keyword(s):  
Differential Equations ◽  
Higher Order ◽  
Lacunary Series ◽  
Linear Differential Equations ◽  
Order Linear ◽  
Iterated Order ◽  
Complex Oscillation ◽  
Linear Differential ◽  
Growth Of Solutions

The authors introduce the lacunary series of finite iterated order and use them to investigate the growth of solutions of higher-order linear differential equations with entire coefficients of finite iterated order and obtain some results which improve and extend some previous results of Belaidi, 2006, Cao and Yi, 2007, Kinnunen, 1998, Laine and Wu, 2000, Tu and Chen, 2009, Tu and Deng, 2008, Tu and Deng, 2010, Tu and Liu, 2009, and Tu and Long, 2009.

scholarly journals GROWTH OF \(\varphi\)–ORDER SOLUTIONS OF LINEAR DIFFERENTIAL EQUATIONS WITH MEROMORPHIC COEFFICIENTS ON THE COMPLEX PLANE

2020 ◽  
Vol 6 (1) ◽  
pp. 95
Author(s):  
Mohamed Abdelhak Kara ◽  
Benharrat Belaïdi
Keyword(s):  
Differential Equations ◽  
Complex Plane ◽  
Higher Order ◽  
Linear Differential Equations ◽  
Order Linear ◽  
Linear Differential ◽  
Growth Of Solutions

In this paper, we study the growth of solutions of higher order linear differential equations with meromorphic coefficients of \(\varphi\)-order on the complex plane. By considering the concepts of \(\varphi\)-order and \(\varphi \)-type, we will extend and improve many previous results due to Chyzhykov–Semochko, Belaïdi, Cao–Xu–Chen, Kinnunen.

scholarly journals On the Iterated Exponent of Convergence of Solutions of Linear Differential Equations with Entire and Meromorphic Coefficients

2013 ◽  
Vol 2013 ◽  
pp. 1-9
Author(s):  
Rabab Bouabdelli ◽  
Benharrat Belaïdi
Keyword(s):  
Differential Equations ◽  
Meromorphic Functions ◽  
Higher Order ◽  
Linear Differential Equations ◽  
Exponent Of Convergence ◽  
Order Linear ◽  
Convergence Of Solutions ◽  
Small Functions ◽  
The Difference ◽  
Linear Differential

We investigate the zeros of the difference of the derivative of solutions of the higher-order linear differential equationsf(k)+Ak-1(z)f(k-1)+⋯+A1(z)f′+A0(z)f=0and small functions, whereA0(z),…,Ak-1(z)are entire or meromorphic functions of finite iteratedporder.

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