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

Jian Deng, Shunsau Nii

研究成果: Contribution to journalArticle査読

8 被引用数 (Scopus)

抄録

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.

本文言語英語
ページ(範囲)753-765
ページ数13
ジャーナルJournal of Differential Equations
244
4
DOI
出版ステータス出版済み - 2 15 2008

All Science Journal Classification (ASJC) codes

  • 分析
  • 応用数学

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