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

 

On principal eigenvalues for boundary value
problems with indefinite weight
and Robin boundary conditions


Authors: G. A. Afrouzi and K. J. Brown
Journal: Proc. Amer. Math. Soc. 127 (1999), 125-130
MSC (1991): Primary 35J15, 35J25
MathSciNet review: 1469392
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Abstract: We investigate the existence of principal eigenvalues (i.e., eigenvalues corresponding to positive eigenfunctions) for the boundary value problem $- \Delta u(x) = \lambda g(x) u(x)$ on $D$; $\frac{\partial u} {\partial n} (x) + \alpha u(x) = 0$ on $\partial D$, where $D$ is a bounded region in $\mathbf{R}^N$, $g$ is an indefinite weight function and $\alpha \in \mathbf{R}$ may be positive, negative or zero.


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Additional Information

G. A. Afrouzi
Affiliation: Department of Mathematics, Faculty of Basic Sciences, Mazandaran University, P.O.Box 311, Babolsar, Iran

K. J. Brown
Affiliation: Department of Mathematics, Heriot-Watt University, Riccarton, Edinburgh EH14 4AS, United Kingdom
Email: K.J.Brown@hw.ac.uk

DOI: http://dx.doi.org/10.1090/S0002-9939-99-04561-X
PII: S 0002-9939(99)04561-X
Keywords: Indefinite weight function, principal eigenvalues
Received by editor(s): April 30, 1997
Additional Notes: The first author gratefully acknowledges financial support from the Ministry of Culture and Higher Education of the Iran Islamic Republic.
Communicated by: Jeffrey B. Rauch
Article copyright: © Copyright 1999 American Mathematical Society