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29.—Finiteness of the Order of Meromorphic Solutions of some Non-linear Ordinary Differential Equations*

Published online by Cambridge University Press:  14 February 2012

Einar Hille
Einar Hille
Affiliation:
Department of Mathematics, University of California, San Diego, La Jolla.
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Synopsis

It is well known that the existence of transcendental meromorphic solutions of non-linear ordinary differential equations puts severe restrictions on the equation, the most striking example being the theorem of Malmquist [3]. The value distribution theory of R. Nevanlinna was applied to such questions by K. Yosida [8] who used it to prove Malmquist's theorem as well as important generalisations. An alternate approach was given by H. Wittich [4,5,6] and in his argument the finiteness of the order played an essential role. Wittich estimated the corresponding enumerative and proximity functions via the calculus of residues. In this note a geometric argument is proposed instead (closest packing of small discs in a bigger circle or on its rim). This method seems to generalise more readily to Yosida's extensions.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 72 , Issue 4 , 1975 , pp. 331 - 336
Copyright
Copyright © Royal Society of Edinburgh 1975

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References

References to Literature

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