Comparison Theorems for Homogeneous Linear Differential Equations of General Order

1918 ◽  
Vol 19 (3) ◽  
pp. 159
Author(s):  
R. D. Carmichael
Keyword(s):  
Differential Equations ◽  
Linear Differential Equations ◽  
Comparison Theorems ◽  
General Order ◽  
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.

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