Principal eigenvalues for indefinite weight problems in all of ℝ^{𝕕}

Rhouma, N.

doi:10.1090/S0002-9939-03-06967-3

Principal eigenvalues for indefinite weight problems in all of $\mathbb {R}^{d}$
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by N. Bejhaj Rhouma PDF

Proc. Amer. Math. Soc. 131 (2003), 3747-3755 Request permission

Abstract:

We show the existence of principal eigenvalues of the problem $-\triangle u=\lambda gu$ in $\mathbb {R}^{d}$ where $g$ 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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