Non-symmetric low-index solutions for a symmetric boundary value problem
نویسندگان
چکیده
Abstract. We consider the equation −∆u = wu on a square domain in R, with Dirichlet boundary conditions, where w is a given positive function that is invariant under all (Euclidean) symmetries of the square. This equation is shown to have a solution u, 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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Some symmetric boundary value problems and non-symmetric solutions
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