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A test for Picard principle

Published online by Cambridge University Press:  22 January 2016

Mitsuru Nakai
Mitsuru Nakai*
Affiliation:
Nagoya University
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A nonnegative locally Hölder continuous function P(z) on 0 < | z | ≤ 1 will be referred to as a density on 0 < | z | ≤ 1. The elliptic dimension of a density P(z) at z = 0, dim P in notation, is defined to be the dimension of the half module of nonnegative solutions of the equation Δu(z) = P(z)u(z) on the punctured unit disk Ω : 0 < | z | < 1 with boundary values zero on | z | = 1. After Bouligand we say that the Picard principle is valid for a density P at z = 0 if dim P = 1.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 56 , January 1975 , pp. 105 - 119
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1975

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