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

作者：Deng Jian; Nii Shunsau^*

来源：Journal of Differential Equations, 2008, 244(4): 753-765.

DOI：10.1016/j.jde.2007.10.037

• Evans function
• stability index
• Fredholm Grassmannian
• elliptic eigenvalue problems

An infinite-dimensional Evans function E(lambda) and a stability index theorem are developed for the elliptic eigenvalue problem in a bounded domain Omega subset of 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 Omega is star-shaped, an associated unstable bundle epsilon(D) based on D is constructed, and the first Chem number of epsilon(D) also gives the number of eigenvalues of the elliptic operator inside D.

• 出版日期2008-2-15
• 单位中央财经大学