A Counterexample to the Nodal Domain Conjecture and a Related Semilinear Equation
Open Access
- 1 February 1988
- journal article
- Published by JSTOR in Proceedings of the American Mathematical Society
- Vol. 102 (2) , 271-277
- https://doi.org/10.2307/2045874
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 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 .Keywords
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