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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Principal eigenvalues for indefinite weight problems in all of $\mathbb{R}^{d}$


Author: N. Bejhaj Rhouma
Journal: Proc. Amer. Math. Soc. 131 (2003), 3747-3755
MSC (2000): Primary 31B20, 35J25, 35P05
Published electronically: February 14, 2003
MathSciNet review: 1998182
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Abstract: We show the existence of principal eigenvalues of the problem $-\triangle u=\lambda gu$ in $\mathbb{R}^{d}$ where $g$ is an indefinite weight function. The existence of a continuous family of principal eigenvalues is demonstrated. Also, we prove the existence of a principal eigenvalue for which the principal eigenfunction $u\rightarrow 0$ at $\infty$.


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Additional Information

N. Bejhaj Rhouma
Affiliation: Institut Préparatoire aux Études d’Ingénieurs de Tunis, 2, rue Jawaherlel Nehru, 1008 Montfleury, Tunis, Tunisia
Email: Nedra.BelHajRhouma@ipeit.rnu.tn

DOI: http://dx.doi.org/10.1090/S0002-9939-03-06967-3
PII: S 0002-9939(03)06967-3
Keywords: Indefinite weight, eigenvalue, Kato-class, Green function
Received by editor(s): November 20, 2001
Received by editor(s) in revised form: June 25, 2002
Published electronically: February 14, 2003
Communicated by: Juha M. Heinonen
Article copyright: © Copyright 2003 American Mathematical Society