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A further result on the complex oscillation theory of periodic second order linear differential equations*

Published online by Cambridge University Press:  20 January 2009

Shian Gao
Shian Gao
Affiliation:
Department of Mathematics, South China Normal University, Guangzhou, P. R. China
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Abstract

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We prove the following: Assume that , where p is an odd positive integer, g(ζ is a transcendental entire function with order of growth less than 1, and set A(z) = B(ezz). Then for every solution , the exponent of convergence of the zero-sequence is infinite, and, in fact, the stronger conclusion holds. We also give an example to show that if the order of growth of g(ζ) equals 1 (or, in fact, equals an arbitrary positive integer), this conclusion doesn't hold.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 33 , Issue 1 , February 1990 , pp. 143 - 158
Copyright
Copyright © Edinburgh Mathematical Society 1990

References

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