Nonlinear Eigenvalue Problems on Infinite Intervals.
Abstract
This paper is concerned with nonlinear eigenvalue problems of boundary value problems for ordinary differential equation posed on an infinite interval. It is shown that under certain analyticity assumptions - a domain in the complex plain can be identified, in which all eigenvalues are isolated. An intriguing way to solve such problems is to cut the infinite interval at a finite but large enough point and to impose additional, so called asymptotic boundary conditions at this far end. The obtained eigenvalue problem for the two point boundary value problem on this finite but large interval can be solved by an appropriate code. In this paper suitable asymptotic boundary conditions are devised and the order of convergence, as the length of the interval, on which these approximating problems are posed, converges to infinity, is investigated. Exponential convergence is shown for well posed approximating problems. (Author)
Document Details
- Document Type
- Technical Report
- Publication Date
- Apr 01, 1981
- Accession Number
- ADA100624
Entities
People
- Peter A. Markowich
- Richard G. Weiss
Organizations
- University of Wisconsin–Madison