We consider the equation −Delta u = wu3 on a square domain in R2, 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.

Non-symmetric low-index solutions for a symmetric boundary value problem

ARIOLI, GIANNI;
2012-01-01

Abstract

We consider the equation −Delta u = wu3 on a square domain in R2, 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.
2012
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11311/619172
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