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 &Delta;<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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