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Holomorphic solutions about an irregular singular point of an ordinary linear differential equation

Part of: Qualitative theory General theory in ordinary differential equations

Published online by Cambridge University Press:  09 April 2009

C. E. M. Pearce
C. E. M. Pearce
Affiliation:
Department of Applied MathematicsThe University of Adelaide Adelaide, S. A. 5001, Australia
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Abstract

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It is shown that that an ordinary linear differential equation may possess a holomorphic solution in a neighbourhood of an irregular singular point even though the usual linearly independent solutions corresponding to the two roots of the indicial equation both have zero radius of convergence.

MSC classification

Secondary: 34C05: Location of integral curves, singular points, limit cycles 34A25: Analytical theory
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 39 , Issue 2 , October 1985 , pp. 178 - 186
Copyright
Copyright © Australian Mathematical Society 1985

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