On the connectivity properties of the solution set of parametrized families of compact vector fields
type: Item
instance of: scholarly article
title: On the connectivity properties of the solution set of parametrized families of compact vector fields
zbMATH Open document ID: 0562.47048
DOI: 10.1016/0022-1236(84)90069-7
author: Ivar Massabò
author: Jacobo Pejsachowicz
published in: Journal of Functional Analysis
publication date: 1984-01-01T00:00:00Z
review text: An extension to n-parameter families of compact vector fields of the well-known Leray-Schauder continuation principle is obtained. Using Čech cohomology, it is proved that (under the usual assumptions) the zero-set of the family contains a closed connected subset of dimension at least n whose projection covers all of the parameters space. See also [\textit{P. M. Fitzpatrick} and the authors Math. Ann. 263, 61-73 (1983; Zbl 0519.58024)].
Mathematics Subject Classification ID: 47J05
Mathematics Subject Classification ID: 58E07
zbMATH DE Number: 3895732
zbMATH Keywords: n-parameter families of compact vector fields
zbMATH Keywords: Leray-Schauder continuation principle
zbMATH Keywords: Čech cohomology
zbMATH Keywords: zero-set
MaRDI profile type: Publication
full work available at URL: 0022-1236(84)90069-7
OpenAlex ID: W2171945949
cites work: Global and local behavior of bifurcating multidimensional continua of solutions for multiparameter nonlinear eigenvalue problems
cites work: The implicit function theorem and the global methods of cohomology
cites work: Elliptic equations with noninvertible Fredholm linear part and bounded nonlinearities
cites work: On a free boundary problem arising in plasma physics
cites work: Seminar on Transformation Groups. (AM-46)
cites work: Q4167193
cites work: Q3286050
cites work: Q5341132
cites work: Q5643279
cites work: The fixed point transfer of fiber-preserving maps
cites work: Ordinary differential equations with nonlinear boundary conditions
cites work: Q5557005
cites work: Q4056996
cites work: A nonlinear elliptic boundary value problem at resonance
cites work: Q5522742
cites work: Some Bifurcation Theory for k -Set Contractions
description: scientific article; zbMATH DE number 3895732