Accession Number : AD0712438

Title :   BIFURCATION FROM SIMPLE EIGENVALUES,

Corporate Author : CALIFORNIA UNIV LOS ANGELES DEPT OF MATHEMATICS

Personal Author(s) : Crandall,Michael G. ; Rabinowitz,Paul H.

Report Date : SEP 1970

Pagination or Media Count : 35

Abstract : Let G be a mapping of a subset of a Banach space W into a Banach space Y. Let C be a curve in W such that G(C) = (0). A general version of the main problem of bifurcation theory may be stated: Given p epsilon C, determine the structure of G sup (-1) (0) in some neighborhood of p. In this work simple conditions are given under which there is a neighborhood N sub p of p such that (G sup (-1))(0) intersection (N sub p) is topologically (or diffeomorphically) equivalent to the subset (-1,1)x(0) intersection (0)x(-1,1) of the plane, and the first order behavior of G on (G sup (-1))(0) intersection (N sub p) as well as the set itself is studied. The results obtained give a new unity to that part of bifurcation theory commonly called 'bifurcation from a simple eigenvalue' as well as extend its applicability. A broad spectrum of examples is offered, including some generalizations of known results concerning non-linear eigenvalue problems for ordinary and partial differential equations. (Author)

Descriptors :   (*NONLINEAR DIFFERENTIAL EQUATIONS, *BOUNDARY VALUE PROBLEMS), (*MAPPING(TRANSFORMATIONS), BANACH SPACE), PARTIAL DIFFERENTIAL EQUATIONS, TOPOLOGY, THEOREMS

Subject Categories : Theoretical Mathematics

Distribution Statement : APPROVED FOR PUBLIC RELEASE