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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Nonmonotoneity of Picard principle


Authors: Mitsuru Nakai and Toshimasa Tada
Journal: Trans. Amer. Math. Soc. 292 (1985), 629-644
MSC: Primary 30F25
MathSciNet review: 808742
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Abstract: Two nonnegative $ {C^\infty }$ functions $ P(z)$ and $ Q(z)$ on the punctured unit disk $ 0 < \vert z\vert \leqslant 1$ are constructed such that $ Q(z) \leqslant P(z)$ and there exists only one Martin minimal boundary point for the equation $ \Delta u = Pu$ over $ z = 0$ and, nevertheless, there exist exactly two Martin minimal boundary points for the equation $ \Delta u = Qu$ over $ z = 0$.


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DOI: http://dx.doi.org/10.1090/S0002-9947-1985-0808742-7
PII: S 0002-9947(1985)0808742-7
Article copyright: © Copyright 1985 American Mathematical Society