# An infinite-dimensional Evans function theory for elliptic boundary value problems

- Authors
- Journal
- Journal of Differential Equations 0022-0396
- Publisher
- Elsevier
- Publication Date
- Volume
- 244
- Issue
- 4
- Identifiers
- DOI: 10.1016/j.jde.2007.10.037
- Keywords
- Disciplines

## Abstract

Abstract An infinite-dimensional Evans function E ( λ ) and a stability index theorem are developed for the elliptic eigenvalue problem in a bounded domain Ω ⊂ R m . The number of zero points of the Evans function in a bounded, simply connected complex domain D is shown to be equal to the number of eigenvalues of the corresponding elliptic operator in D. When the domain Ω is star-shaped, an associated unstable bundle E ( D ) based on D is constructed, and the first Chern number of E ( D ) also gives the number of eigenvalues of the elliptic operator inside D.

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