Remote Access Transactions of the American Mathematical Society
Green Open Access

Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



Elliptic problems involving an indefinite weight

Author: M. Faierman
Journal: Trans. Amer. Math. Soc. 320 (1990), 253-279
MSC: Primary 35P10; Secondary 35J40
MathSciNet review: 962280
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: We consider a selfadjoint elliptic eigenvalue problem, which is derived formally from a variational problem, of the form $ Lu = \lambda \omega (x)u$ in $ \Omega$, $ {B_j}u = 0$ on $ \Gamma $, $ j = 1, \ldots ,m$, where $ L$ is a linear elliptic operator of order $ 2m$ defined in a bounded open set $ \Omega \subset {{\mathbf{R}}^n}\quad (n \geq 2)$ with boundary $ \Gamma$, the $ {B_j}$ are linear differential operators defined on $ \Gamma$, and $ \omega$ is a real-valued function assuming both positive and negative values. For our problem we prove the completeness of the eigenvectors and associated vectors in two function spaces which arise naturally in such an indefinite problem. We also establish some results concerning the eigenvalues of the problem which complement the known results and investigate the structure of the principal subspaces.

References [Enhancements On Off] (What's this?)

Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 35P10, 35J40

Retrieve articles in all journals with MSC: 35P10, 35J40

Additional Information

Keywords: Elliptic boundary value problems, indefinite weight function, eigenvalues, eigenvectors, associated vectors, completeness, Pontrjagin space
Article copyright: © Copyright 1990 American Mathematical Society

American Mathematical Society