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Proceedings of the American Mathematical Society

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

 

 

Principal eigenvalues for indefinite-weight elliptic problems in $ {\bf R}\sp n$


Author: W. Allegretto
Journal: Proc. Amer. Math. Soc. 116 (1992), 701-706
MSC: Primary 35P05; Secondary 35J10, 47F05
DOI: https://doi.org/10.1090/S0002-9939-1992-1098396-9
MathSciNet review: 1098396
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Abstract: We consider the problem $ - \Delta u = \lambda gu$ in $ {R^n}$, $ u \to 0$ at $ \infty $ with $ g$ a function that changes sign. Under suitable growth conditions on $ g$ we show that this problem has an eigenvalue $ \lambda $ with a positive solution $ u$, as well as countably many other eigenvalues.


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DOI: https://doi.org/10.1090/S0002-9939-1992-1098396-9
Keywords: Elliptic equation, indefinite weight, eigenvalue
Article copyright: © Copyright 1992 American Mathematical Society