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Some local properties of the solutions of second-order differential equations

Part of: Entire and meromorphic functions, and related topics

Published online by Cambridge University Press:  09 April 2009

Jiuyi Cheng  and
John Rossi
Jiuyi Cheng
Affiliation:
Department of Mathematics, Virginia Polytechnic Institute and State University, Blacksburg, VA 24061, USA, e-mail: rossi@math.vt.edu
John Rossi
Affiliation:
Department of Mathematics, Virginia Polytechnic Institute and State University, Blacksburg, VA 24061, USA, e-mail: rossi@math.vt.edu
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Abstract

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We investigate the asymptotics and zero distribution of solutions of ω″ + Aω = 0 where A is an entire function of very slow growth. The results parallel the classical case when A is assumed to be a polynomial.

MSC classification

Secondary: 30D35: Distribution of values, Nevanlinna theory
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 59 , Issue 2 , October 1995 , pp. 255 - 265
Copyright
Copyright © Australian Mathematical Society 1995

References

[1]Hayman, W. K., ‘The local growth of power series: a survey of the Wiman-Valiron method’, Canad. Math. Bull. 17 (1974), 317–358.CrossRefGoogle Scholar
[2]Hille, E., ‘Oscillation theorems in the complex domain’, Trans. Amer. Math. Soc. 23 (1922), 350–385.CrossRefGoogle Scholar
[3]Hille, E., Lectures on ordinary differential equations (Addison-Wesley, London, 1969).Google Scholar
[4]Langley, J. K., ‘Proof of a conjecture of Hayman concerning f and f″’, preprint.Google Scholar