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

Chang Shou Lin; Wei Ming Ni

doi:10.1090/S0002-9939-1988-0920985-9

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

Chang Shou Lin, Wei Ming Ni

Mathematics

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68 Scopus citations

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 Schridinger operator on a domain O 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 Ω.

Original language	English (US)
Pages (from-to)	271-277
Number of pages	7
Journal	Proceedings of the American Mathematical Society
Volume	102
Issue number	2
DOIs	https://doi.org/10.1090/S0002-9939-1988-0920985-9
State	Published - Feb 1988

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title = "A counterexample to the nodal domain conjecture and a related semilinear equation",

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 Schridinger operator on a domain O 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 Ω.",

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AU - Ni, Wei Ming

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AB - 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 Schridinger operator on a domain O 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 Ω.

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

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