Non-Linear Sturm-Liouville Problems with No Secondary Bifurcation.
Abstract
The paper is concerned with giving sufficient conditions that in the non-linear boundary-value problem u'(x) + (q(x) + G(x,u(x), lambda))u(x) = 0 with u(0) = 0, u(1) = 0 or u'(1) = 0 there should be no secondary bifurcation, i.e. that, given a branch of solutions (u, lambda) bifurcating from the trivial solution, there should be no further bifurcation on that branch. Sufficient conditions on G are given which include, for example, Kolodner's problem of the motion of a heavy rotating string. (Author)
Document Details
- Document Type
- Technical Report
- Publication Date
- Sep 01, 1977
- Accession Number
- ADA049399
Entities
People
- C. A. Stuart
- J. B. Mcleod
Organizations
- University of Wisconsin–Madison