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

Published online by Cambridge University Press:  20 January 2009

Gao Shi-An
Gao Shi-An
Affiliation:
Department of Mathematics, South China Normal University, Guangzhou, 510631, People's Republic of China
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Abstract

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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.

Keywords

differential equationentire coefficientcomplex oscillation
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 43 , Issue 1 , February 2000 , pp. 1 - 13
Copyright
Copyright © Edinburgh Mathematical Society 2000

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