Partial Differential Equations
Schrödinger equations with indefinite weights in the whole space

Presented by: Jean-Michel Bony

Cardoulis, Laure1
1 Université de Toulouse, UT1 CEREMATH, CNRS, institut de mathématiques de Toulouse, UMR 5219, 21, allées de Brienne, 31042 Toulouse, France
Comptes Rendus. Mathématique, Volume 347 (2009) no. 21-22, pp. 1255-1260.

We consider in this Note equations defined in RN involving Schrödinger operators with indefinite weight functions and with potentials which tend to infinity at infinity. We give some results for the existence of principal eigenvalues and for the maximum principle. We also obtain Courant–Fischer formulas for such eigenvalues.

On considère dans cette Note des équations définies sur RN avec des opérateurs de Schrödinger à poids indéfinis dont les potentiels tendent vers l'infini à l'infini. On donne des résultats pour l'existence de valeurs propres principales ainsi que pour le principe du maximum. On obtient aussi des formules de type Courant–Fischer pour ces valeurs propres.

Received:
Accepted:
Published online:
DOI: 10.1016/j.crma.2009.09.016
Cardoulis, Laure 1

1 Université de Toulouse, UT1 CEREMATH, CNRS, institut de mathématiques de Toulouse, UMR 5219, 21, allées de Brienne, 31042 Toulouse, France 
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Cardoulis, Laure. Schrödinger equations with indefinite weights in the whole space. Comptes Rendus. Mathématique, Volume 347 (2009) no. 21-22, pp. 1255-1260. doi : 10.1016/j.crma.2009.09.016. http://www.numdam.org/articles/10.1016/j.crma.2009.09.016/

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