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Minimax Theory and its Applications 07 (2022), No. 2, 365--380
Copyright Heldermann Verlag 2022

A Computer Assisted Proof of the Symmetries of Least Energy Nodal Solutions on Squares

Ariel Salort
(1) Dep. de Matemática, FCEyN, Universidad de Buenos Aires, Argentina
(2) IMAS - CONICET, Buenos Aires, Argentina

Christophe Troestler
Dép. de Mathématique, Université de Mons, Belgium


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 $-\Delta u = |u|^{p-2} u$ 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 $2$.

Keywords: Least energy sign changing solutions, symmetries, interval arithmetic, verified computation.

MSC: 35J20; 35B06, 65G40.

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