A note on the complex oscillation theory of non- homogeneous linear differential equations

1990 ◽  
Vol 18 (3-4) ◽  
pp. 282-285 ◽  
Author(s):  
Ilpo Laine
Keyword(s):  
Differential Equations ◽  
Oscillation Theory ◽  
Linear Differential Equations ◽  
Complex Oscillation ◽  
Linear Differential ◽  
Homogeneous Linear

scholarly journals On the complex oscillation for a class of homogeneous linear differential equations

2000 ◽  
Vol 43 (1) ◽  
pp. 1-13 ◽  
Author(s):  
Gao Shi-An
Keyword(s):  
Differential Equations ◽  
Open Problem ◽  
Linear Differential Equations ◽  
Unique Case ◽  
Linearly Independent ◽  
Complex Oscillation ◽  
Linear Differential ◽  
Dominant Condition ◽  
Homogeneous Linear ◽  
Independent Zero

AbstractUsing a combined dominant condition, we obtain general results concerning the complex oscillation for a class of homogeneous linear differential equations w(k) + + … + A1w′ + (A0 + A)w = 0 with k ≥ 2, which has been investigated by many authors. In particular, we discover that there exists a unique case that possesses k linearly independent zero-free solutions for these equations, and we resolve an open problem and simultaneously answer a question of Bank.

Growth and oscillation theory of non-homogeneous linear differential equations

2000 ◽  
Vol 43 (2) ◽  
pp. 343-359 ◽  
Author(s):  
Gary G. Gundersen ◽  
Enid M. Steinbart ◽  
Shupei Wang
Keyword(s):  
Differential Equation ◽  
Entire Function ◽  
Differential Equations ◽  
Finite Order ◽  
Oscillation Theory ◽  
Linear Differential Equations ◽  
Linear Differential ◽  
Homogeneous Linear

AbstractWe investigate the growth and the frequency of zeros of the solutions of the differential equation f(n) + Pn–1 (z) f(n–1) + … + P0 (z) f = H (z), where P0 (z), P1(z), …, Pn–1(z) are polynomials with P0 (z) ≢ 0, and H (z) ≢ 0 is an entire function of finite order.

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