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

Authors: N. Rhouma;

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

Abstract

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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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
2
Average
Average
Average
hybrid