Calculus of Variations and Geometric Measure Theory

D. Bartolucci - A. Jevnikar - J. Jin - C. S. Lin - S. Liu

Non-degeneracy and uniqueness of solutions to general singular Toda systems on bounded domains

created by jevnikar on 24 Jul 2022
modified on 14 Feb 2023


Accepted Paper

Inserted: 24 jul 2022
Last Updated: 14 feb 2023

Journal: J. Math. Anal. Appl.
Pages: 17
Year: 2023


In this note we show non-degeneracy and uniqueness results for solutions of Toda systems associated to general simple Lie algebras with multiple singular sources on bounded domains. The argument is based on spectral properties of Cartan matrices and eigenvalue analysis of linearized Liouville-type problems. This seems to be the first result for this class of problems and it covers all the Lie algebras of any rank.

Keywords: uniqueness, Toda system, Non-degeneracy, Simple Lie algebra, Linearized problem