PERIODIC SYSTEMS OF THE PERTURBATION TYPE: SMALL PARAMETER BOUNDS.
Interim technical rept. 29 Oct 64-29 Oct 65.
SYRACUSE UNIV N Y
Pagination or Media Count:
Bounds on the small parameter of systems of the perturbation type are developed to insure existence of periodic solutions. Solutions sought are in k, the space of functions which are periodic in time, t, of period T and are Lebesque square integrable over a period. The procedure follows the general framework of the Hale-Cesari technique. A projection operator, suitably defined on k, is used to decompose the problem into two parts, an associated equation and a bifurcation equation. Iteration procedures are developed for both the associated equation and the bifurication equation. The tools of functional analysis and, in particular, the Contraction Mapping Fixed Point Theorem are used to establish bounds on the small parameter, beta, to insure the convergence of each of the iteration procedures. The smaller of the two bounds obtained is recognized as the value which insures solution to the overall system. Author
- Theoretical Mathematics