
We show the existence of principal eigenvalues of the problem − △ u = λ g u -\triangle u=\lambda gu in R d \mathbb {R}^{d} where g 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 → 0 u\rightarrow 0 at ∞ \infty .
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