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

Chang Shou Lin, Wei Ming Ni

Research output: Contribution to journalArticle

62 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 languageEnglish (US)
Pages (from-to)271-277
Number of pages7
JournalProceedings of the American Mathematical Society
Volume102
Issue number2
DOIs
StatePublished - Feb 1988

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