Principal eigenvalues for problems with indefinite weight function on $\textbf {R}^ n$
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- by K. J. Brown, C. Cosner and J. Fleckinger PDF
- Proc. Amer. Math. Soc. 109 (1990), 147-155 Request permission
Abstract:
We investigate the existence of positive principal eigenvalues of the problem $- \Delta u(x) = \lambda g(x)u$ for $x \in {R^n};u(x) \to 0$ as $x \to \infty$ where the weight function $g$ changes sign on ${R^n}$. It is proved that such eigenvalues exist if $g$ is negative and bounded away from 0 at $\infty$ or if $n \geq 3$ and $|g(x)|$ is sufficiently small at $\infty$ but do not exist if $n = 1 {\text {or}} 2$ and $\int _{{R^n}} {g(x)dx > 0}$.References
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Additional Information
- © Copyright 1990 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 109 (1990), 147-155
- MSC: Primary 35P05; Secondary 35J25
- DOI: https://doi.org/10.1090/S0002-9939-1990-1007489-1
- MathSciNet review: 1007489