The classical Poincaré–Bohl theorem provides the existence of a zero for a function avoiding external rays. When the domain is convex, the same holds true when avoiding normal cones. We consider here the possibility of dealing with nonconvex sets having inward corners or cusps, in which cases the normal cone vanishes. This allows us to deal with situations where the topological degree may be strictly greater than 1.

On the topological degree of planar maps avoiding normal cones / Fonda, A.; Klun, G.. - In: TOPOLOGICAL METHODS IN NONLINEAR ANALYSIS. - ISSN 1230-3429. - 53:2(2019), pp. 825-845. [10.12775/TMNA.2019.034]

On the topological degree of planar maps avoiding normal cones

Klun, G.
2019-01-01

Abstract

The classical Poincaré–Bohl theorem provides the existence of a zero for a function avoiding external rays. When the domain is convex, the same holds true when avoiding normal cones. We consider here the possibility of dealing with nonconvex sets having inward corners or cusps, in which cases the normal cone vanishes. This allows us to deal with situations where the topological degree may be strictly greater than 1.
2019
53
2
825
845
http://preprints.sissa.it/xmlui/handle/1963/35330
Fonda, A.; Klun, G.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/20.500.11767/90593
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