Periodic and Quasiperiodic Solutions of Delta u + Lambda u + 0(u) = 0.
Abstract
In this paper the boundary value problems Delta u + lambda u+f(u, u(x), U)y))=0, u(0,y)=u(1,y)-0 is studied in the strip (0,1)xR, where f is some C(superscript 2)-function which, together with its gradient, vanishes at 0, lambda is a real parameter. It is shown that, for lambda between pi-squared and 4 pi-squared all small solutions are periodic in y. Moreover, singular solutions exist as local H(superscript 2)-limits of periodic solutions with large periods. For values of lambda beyond 4 pi-squared a formal argument suggests that almost all small solutions are quasiperiodic. The equation is studied as a model for some important but technically cumbersome bifurcation problems in fluid dynamics. (Author)
Document Details
- Document Type
- Technical Report
- Publication Date
- Aug 01, 1977
- Accession Number
- ADA046435
Entities
People
- Juergen Scheurle
- Klaus Kirchgaessner
Organizations
- University of Wisconsin–Madison