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.File | Dimensione | Formato | |
---|---|---|---|
TMNA2386.pdf
non disponibili
Tipologia:
Versione Editoriale (PDF)
Licenza:
Tutti i diritti riservati (All rights reserved)
Dimensione
421.4 kB
Formato
Adobe PDF
|
421.4 kB | Adobe PDF | Visualizza/Apri Richiedi una copia |
Fonda-Klun_revised.pdf
Open Access dal 18/05/2020
Tipologia:
Documento in Post-print
Licenza:
Non specificato
Dimensione
436.62 kB
Formato
Adobe PDF
|
436.62 kB | Adobe PDF | Visualizza/Apri |
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.