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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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On the Neumann problem for some semilinear elliptic equations and systems of activator-inhibitor type
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by Wei-Ming Ni and Izumi Takagi PDF
Trans. Amer. Math. Soc. 297 (1986), 351-368 Request permission

Abstract:

We derive a priori estimates for positive solutions of the Neumann problem for some semilinear elliptic systems (i.e., activator-inhibitor systems in biological pattern formation theory), as well as for semilinear single equations related to such systems. By making use of these a priori estimates, we show that under certain assumptions, there is no positive nonconstant solutions for single equations or for activator-inhibitor systems when the diffusion coefficient (of the activator, in the case of systems) is sufficiently large; we also study the existence of nonconstant solutions for specific domains.
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Additional Information
  • © Copyright 1986 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 297 (1986), 351-368
  • MSC: Primary 35J65; Secondary 92A09
  • DOI: https://doi.org/10.1090/S0002-9947-1986-0849484-2
  • MathSciNet review: 849484