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Proceedings of the American Mathematical Society

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A counterexample to the nodal domain conjecture and a related semilinear equation


Authors: Chang Shou Lin and Wei-Ming Ni
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
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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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DOI: https://doi.org/10.1090/S0002-9939-1988-0920985-9
Article copyright: © Copyright 1988 American Mathematical Society