We consider in this Note equations defined in 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 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.
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Laure Cardoulis 1
@article{CRMATH_2009__347_21-22_1255_0, author = {Laure Cardoulis}, title = {Schr\"odinger equations with indefinite weights in the whole space}, journal = {Comptes Rendus. Math\'ematique}, pages = {1255--1260}, publisher = {Elsevier}, volume = {347}, number = {21-22}, year = {2009}, doi = {10.1016/j.crma.2009.09.016}, language = {en}, }
Laure Cardoulis. 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. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2009.09.016/
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