On the singularities of nonlinear fredholm operators of positive index

Authors

M. S. Berger, Institute for Advanced Study
R. A. Plastock, University of Massachusetts Amherst

Document Type

Article

Publication Date

1-1-1980

Abstract

The singular set B = {x|F¹(x) is not surjective} of a nonlinear Fredholm operator F of positive index (between Banach spaces X1 and X2) is investigated. Under the assumption that the mapping is proper and has a locally Lipschitzian Fréchet derivative F¹(x), it is shown that the singular set B is nonempty. Furthermore, when the Banach spaces are infinite dimensional, B cannot be the countable union of compact sets nor can F^-1(F(B)) contain isolated points. © 1980 American Mathematical Society.

Identifier

84966208572 (Scopus)

Publication Title

Proceedings of the American Mathematical Society

External Full Text Location

https://doi.org/10.1090/S0002-9939-1980-0565342-5

e-ISSN

10886826

ISSN

00029939

First Page

217

Last Page

221

Issue

2

Volume

79

Recommended Citation

Berger, M. S. and Plastock, R. A., "On the singularities of nonlinear fredholm operators of positive index" (1980). Faculty Publications. 21423.
https://digitalcommons.njit.edu/fac_pubs/21423