Geodesic
A computer assisted proof of the symmetries of least energy nodal solutions on squares
Minimax theory and its applications, Tome 7 (2022) no. 2
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Using a Lyapunov-Schmidt reduction on an asymptotic Nehari manifold and verified computations, we prove that the least energy nodal solutions to Lane-Emden equation −∆u = |u|p−2u with zero Dirichlet boundary conditions on a square are odd with respect to one diagonal and even with respect to the other one when p is close to 2.
Mots-clés : Least energy sign changing solutions, symmetries, interval arithmetic, verified compu tation 
@article{MTA_2022_7_2_a8,
     author = {Ariel Salort and Christophe Troestler},
     title = {A computer assisted proof of the symmetries of least energy nodal solutions on squares},
     journal = {Minimax theory and its applications},
     year = {2022},
     volume = {7},
     number = {2},
     zbl = {1490.35112},
     url = {http://geodesic.mathdoc.fr/item/MTA_2022_7_2_a8/}
}
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Ariel Salort; Christophe Troestler. A computer assisted proof of the symmetries of least energy nodal solutions on squares. Minimax theory and its applications, Tome 7 (2022) no. 2. http://geodesic.mathdoc.fr/item/MTA_2022_7_2_a8/