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

Authors

  • Ariel Salort, Christophe Troestler Author

Keywords:

Least energy sign changing solutions, symmetries, interval arithmetic, verified compu tation

Abstract

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.

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Published

2022-01-01

Issue

Vol. 7 No. 2 (2022): volume 7 issue 2 (2022)

Section

Articles

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How to Cite

A Computer Assisted Proof of the Symmetries of Least Energy Nodal Solutions on Squares. (2022). Minimax Theory and Its Applications, 7(2), 365–380. https://journalmta.com/index.php/jmta/article/view/172