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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
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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