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LOCALISATION OF LINEAR DIFFERENTIAL EQUATIONS IN THE UNIT DISC BY A CONFORMAL MAP

Part of: Entire and meromorphic functions, and related topics Differential equations in the complex domain

Published online by Cambridge University Press:  15 October 2015

JUHA-MATTI HUUSKO
JUHA-MATTI HUUSKO*
Affiliation:
Department of Physics and Mathematics, University of Eastern Finland, P.O. Box 111, 80101 Joensuu, Finland email [email protected]
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Abstract

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We obtain lower bounds for the growth of solutions of higher order linear differential equations, with coefficients analytic in the unit disc of the complex plane, by localising the equations via conformal maps and applying known results for the unit disc. As an example, we study equations in which the coefficients have a certain explicit exponential growth at one point on the boundary of the unit disc and consider the iterated $M$-order of solutions.

Keywords

complex differential equationsgrowth of solutionsunit disclocalisation

MSC classification

Primary: 34M10: Oscillation, growth of solutions
Secondary: 30D35: Distribution of values, Nevanlinna theory
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 93 , Issue 2 , April 2016 , pp. 260 - 271
Copyright
© 2015 Australian Mathematical Publishing Association Inc. 

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