On the existence of eigenvalues of a divergence-form operator A+ λB in a gap of σ(A)

S. Alama, M. Avellaneda, P. A. Deift, R. Hempel

Research output: Contribution to journalArticle

Abstract

We consider uniformly elliptic divergence type operators A = -SUM ∂jaij(x)∂i with bounded, Lipschitz continuous coefficients, acting in a Hilbert space L2(Rv). It is easy to see that such an operator cannot have discrete eigenvalues below the infimum of the essential spectrum. In order to produce eigenvalues with exponentially decaying eigenfunctions we study a family of operators. In addition, we analyze the connection between decay properties of the coefficient matrix (bij) and the asymptotics of the associated eigenvalue counting function; these results are modeled on our earlier work in the Schrodinger case.

Original languageEnglish (US)
Pages (from-to)311-344
Number of pages34
JournalAsymptotic Analysis
Volume8
Issue number4
StatePublished - Jun 1994

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Hilbert spaces
Eigenvalues and eigenfunctions
Divergence
Eigenvalue
Operator
Counting Function
Essential Spectrum
Coefficient
Eigenfunctions
Lipschitz
Hilbert space
Decay
Form

ASJC Scopus subject areas

  • Applied Mathematics

Cite this

On the existence of eigenvalues of a divergence-form operator A+ λB in a gap of σ(A). / Alama, S.; Avellaneda, M.; Deift, P. A.; Hempel, R.

In: Asymptotic Analysis, Vol. 8, No. 4, 06.1994, p. 311-344.

Research output: Contribution to journalArticle

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