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

Jian Deng, Shunsau Nii

Research output: Contribution to journalArticle

8 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

Fingerprint Dive into the research topics of 'An infinite-dimensional Evans function theory for elliptic boundary value problems'. Together they form a unique fingerprint.

  • Cite this