 10141 Gianni Arioli, Hans Koch
 Nonsymmetric lowindex solutions
for a symmetric boundary value problem
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Sep 9, 10

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Abstract. We consider the equation Δ<i>u=wu</i><sup>3</sup>
on a square domain in R<sup>2</sup>, with Dirichlet boundary conditions,
where <i>w</i> is a given positive function
that is invariant under all (Euclidean) symmetries of the square.
This equation is shown to have a solution <i>u</i>,
with Morse index 2, that is neither symmetric nor antisymmetric
with respect to any nontrivial symmetry of the square.
Part of our proof is computerassisted.
An analogous result is proved for index 1.
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