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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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A counterexample to the nodal domain conjecture and a related semilinear equation
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by Chang Shou Lin and Wei-Ming Ni PDF
Proc. Amer. Math. Soc. 102 (1988), 271-277 Request permission

Abstract:

In this paper we first establish a nonuniqueness result for a semilinear Dirichlet problem of which the nonlinearity is of super-critical growth. We then apply this result to construct a Schrödinger operator on a domain $\Omega$ such that the second eigenfunctions of this operator (with zero Dirichlet boundary data) have their nodal sets completely contained in the interior of the domain $\Omega$.
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Additional Information
  • © Copyright 1988 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 102 (1988), 271-277
  • MSC: Primary 35B05,; Secondary 35J60
  • DOI: https://doi.org/10.1090/S0002-9939-1988-0920985-9
  • MathSciNet review: 920985