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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48.

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Nonmonotoneity of Picard principle
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by Mitsuru Nakai and Toshimasa Tada PDF
Trans. Amer. Math. Soc. 292 (1985), 629-644 Request permission

Abstract:

Two nonnegative ${C^\infty }$ functions $P(z)$ and $Q(z)$ on the punctured unit disk $0 < |z| \leqslant 1$ 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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Additional Information
  • © Copyright 1985 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 292 (1985), 629-644
  • MSC: Primary 30F25
  • DOI: https://doi.org/10.1090/S0002-9947-1985-0808742-7
  • MathSciNet review: 808742