Remote Access Transactions of the American Mathematical Society
Green Open Access

Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



Structure and dimension of global branches of solutions to multiparameter nonlinear equations

Authors: J. Ize, I. Massabò, J. Pejsachowicz and A. Vignoli
Journal: Trans. Amer. Math. Soc. 291 (1985), 383-435
MSC: Primary 58E07; Secondary 47H15
MathSciNet review: 800246
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: This paper is concerned with the topological dimension of global branches of solutions appearing in different problems of Nonlinear Analysis, in particular multiparameter (including infinite dimensional) continuation and bifurcation problems. By considering an extension of the notion of essential maps defined on sets and using elementary point set topology, we are able to unify and extend, in a selfcontained fashion, most of the recent results on such problems. Our theory applies whenever any generalized degree theory with the boundary dependence property may be used, but with no need of algebraic structures. Our applications to continuation and bifurcation follow from the nontriviality of a local invariant, in the stable homotopy group of a sphere, and give information on the local dimension and behavior of the sets of solutions, of bifurcation points and of continuation points.

References [Enhancements On Off] (What's this?)

Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 58E07, 47H15

Retrieve articles in all journals with MSC: 58E07, 47H15

Additional Information

Keywords: Global branches of solutions, multiparameter continuation problems, multiparameter bifurcation problems, covering dimension, essential maps, cantor manifolds
Article copyright: © Copyright 1985 American Mathematical Society