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

Jian Deng, Shunsau Nii

    Research output: Contribution to journalArticlepeer-review

    11 Citations (Scopus)

    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 ⊂ Rm. 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.

    Original languageEnglish
    Pages (from-to)753-765
    Number of pages13
    JournalJournal of Differential Equations
    Volume244
    Issue number4
    DOIs
    Publication statusPublished - Feb 15 2008

    All Science Journal Classification (ASJC) codes

    • Analysis
    • Applied Mathematics

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