TY - JOUR

T1 - An infinite-dimensional Evans function theory for elliptic boundary value problems

AU - Deng, Jian

AU - Nii, Shunsau

N1 - Funding Information:
* Corresponding author. E-mail addresses: jdeng@fudan.edu.cn (J. Deng), snii@math.kyushu-u.ac.jp (S. Nii). 1 Partially supported by Grant-in-Aid for Young Scientists (B) (K AKENHI 14740112), The Ministry of Education, Culture, Sports, Science and Technology.

PY - 2008/2/15

Y1 - 2008/2/15

N2 - 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.

AB - 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.

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U2 - 10.1016/j.jde.2007.10.037

DO - 10.1016/j.jde.2007.10.037

M3 - Article

AN - SCOPUS:38349019667

SN - 0022-0396

VL - 244

SP - 753

EP - 765

JO - Journal of Differential Equations

JF - Journal of Differential Equations

IS - 4

ER -