# Accession Number:

## AD0712438

# Title:

## BIFURCATION FROM SIMPLE EIGENVALUES,

# Descriptive Note:

# Corporate Author:

## CALIFORNIA UNIV LOS ANGELES DEPT OF MATHEMATICS

# Personal Author(s):

# Report Date:

## 1970-09-01

# Pagination or Media Count:

## 35.0

# 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 GC 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 -10 intersection N sub p is topologically or diffeomorphically equivalent to the subset -1,1x0 intersection 0x-1,1 of the plane, and the first order behavior of G on G sup -10 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:

# Subject Categories:

- Theoretical Mathematics