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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 | References | Similar Articles | Additional Information

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.

References [Enhancements On Off] (What's this?)

  • 1. Robert A. Adams, Sobolev spaces, Academic Press [A subsidiary of Harcourt Brace Jovanovich, Publishers], New York-London, 1975. Pure and Applied Mathematics, Vol. 65. MR 0450957
  • 2. M. Bôcher, The smallest characteristic numbers in a certain exceptional case, Bull. Amer. Math. Soc., 21, (1914), 6-9.
  • 3. W. H. Fleming, A selection-migration model in population genetics, J. Math. Biol. 2 (1975), no. 3, 219–233. MR 0403720
  • 4. Peter Hess and Tosio Kato, On some linear and nonlinear eigenvalue problems with an indefinite weight function, Comm. Partial Differential Equations 5 (1980), no. 10, 999–1030. MR 588690, 10.1080/03605308008820162
  • 5. Joel Smoller, Shock waves and reaction-diffusion equations, Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Science], vol. 258, Springer-Verlag, New York-Berlin, 1983. MR 688146

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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

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