Proceedings of the American Mathematical Society

Author(s): N. Bejhaj Rhouma
Journal: Proc. Amer. Math. Soc. 131 (2003), 3747-3755.
MSC (2000): Primary 31B20, 35J25, 35P05
Posted: February 14, 2003
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Abstract: We show the existence of principal eigenvalues of the problem $-\triangle u=\lambda gu$ in $\mathbb{R}^{d}$ where

is an indefinite weight function. The existence of a continuous family of principal eigenvalues is demonstrated. Also, we prove the existence of a principal eigenvalue for which the principal eigenfunction $u\rightarrow 0$ at $\infty$ .

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