- 10-141 Gianni Arioli, Hans Koch
- Non-symmetric low-index solutions
for a symmetric boundary value problem
(1899K, plain TeX, with eps figures)
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 computer-assisted.
An analogous result is proved for index 1.
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