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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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On principal eigenvalues for boundary value problems with indefinite weight and Robin boundary conditions
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by G. A. Afrouzi and K. J. Brown PDF
Proc. Amer. Math. Soc. 127 (1999), 125-130 Request permission

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
  • 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
  • © Copyright 1999 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 127 (1999), 125-130
  • MSC (1991): Primary 35J15, 35J25
  • DOI: https://doi.org/10.1090/S0002-9939-99-04561-X
  • MathSciNet review: 1469392