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On the complex oscillation for a class of homogeneous linear differential equations
Gao Shi-An
Journal:

Proceedings of the Edinburgh Mathematical Society / Volume 43 / Issue 1 / February 2000

Published online by Cambridge University Press:

20 January 2009, pp. 1-13
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Using 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.