Journal
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS
Volume 65, Issue 1, Pages 175-209Publisher
PERGAMON-ELSEVIER SCIENCE LTD
DOI: 10.1016/j.na.2005.09.010
Keywords
set-valued map; degree theory; equilibrium; constrained problems; continuation; bifurcation
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In the paper we construct a topological degree theory for (single and convex-valued) tangent vector fields defined on locally compact closed subsets of a Banach space. The obtained homotopy invariant is an extension of the classical degree for vector fields on manifolds. The degree allows to study vector fields on sets which are neither smooth nor convex and may be applied to study continuation and bifurcation of equilibria in parameterized families of closed sets. (c) 2005 Elsevier Ltd. All rights reserved.
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