A Note on the Growth of Solutions of Second-Order Complex Linear Differential Equations

2019 ◽  
Vol 43 (3) ◽  
pp. 2137-2150
Author(s):  
Jianyong Qiao ◽  
Qi Zhang ◽  
Jianren Long ◽  
Yezhou Li
Keyword(s):  
Differential Equations ◽  
Second Order ◽  
Linear Differential Equations ◽  
Order Complex ◽  
Complex Linear ◽  
Linear Differential ◽  
Growth Of Solutions

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.

scholarly journals On the Growth of Higher Order Complex Linear Differential Equations Solutions with Entire and Meromorphic Coefficients

Mathematics ◽  
2020 ◽  
Vol 9 (1) ◽  
pp. 58
Author(s):  
Luis Manuel Sánchez Ruiz ◽  
Sanjib Kumar Datta ◽  
Samten Tamang ◽  
Nityagopal Biswas
Keyword(s):  
Differential Equations ◽  
Unknown Function ◽  
Higher Order ◽  
Linear Differential Equations ◽  
Order Complex ◽  
Growth Order ◽  
Order Linear ◽  
Complex Linear ◽  
Linear Differential

We revisit the problem of studying the solutions growth order in complex higher order linear differential equations with entire and meromorphic coefficients of p,q-order, proving how it is related to the growth of the coefficient of the unknown function under adequate assumptions. Our study improves the previous results due to J. Liu - J. Tu - L. Z Shi, L.M. Li - T.B. Cao, and others.

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