Differential and Integral Equations

On Dancer's fixed point index formulas

Yihong Du

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Abstract

Whether Dancer's fixed point index formulas for compact maps hold true for maps which are strict-set-contractions has been an open problem. We show that this problem has a positive answer. This implies in particular that these formulas are applicable to many differential equation systems where the underlying domain is the whole~$R^n$.

Article information

Source
Differential Integral Equations Volume 13, Number 1-3 (2000), 145-158.

Dates
First available in Project Euclid: 21 December 2012

Permanent link to this document
https://projecteuclid.org/euclid.die/1356124294

Mathematical Reviews number (MathSciNet)
MR1811953

Zentralblatt MATH identifier
0977.47047

Subjects
Primary: 47H11: Degree theory [See also 55M25, 58C30]
Secondary: 47H09: Contraction-type mappings, nonexpansive mappings, A-proper mappings, etc.

Citation

Du, Yihong. On Dancer's fixed point index formulas. Differential Integral Equations 13 (2000), no. 1-3, 145--158. https://projecteuclid.org/euclid.die/1356124294.


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