The coincidence index for fundamentally contractible multivalued maps with nonconvex values

Dorota Gabor

Annales Polonici Mathematici (2000)

  • Volume: 75, Issue: 2, page 143-166
  • ISSN: 0066-2216

Abstract

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We study a coincidence problem of the form A(x) ∈ ϕ (x), where A is a linear Fredholm operator with nonnegative index between Banach spaces and ϕ is a multivalued A-fundamentally contractible map (in particular, it is not necessarily compact). The main tool is a coincidence index, which becomes the well known Leray-Schauder fixed point index when A=id and ϕ is a compact singlevalued map. An application to boundary value problems for differential equations in Banach spaces is given.

How to cite

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Gabor, Dorota. "The coincidence index for fundamentally contractible multivalued maps with nonconvex values." Annales Polonici Mathematici 75.2 (2000): 143-166. <http://eudml.org/doc/208391>.

@article{Gabor2000,
abstract = {We study a coincidence problem of the form A(x) ∈ ϕ (x), where A is a linear Fredholm operator with nonnegative index between Banach spaces and ϕ is a multivalued A-fundamentally contractible map (in particular, it is not necessarily compact). The main tool is a coincidence index, which becomes the well known Leray-Schauder fixed point index when A=id and ϕ is a compact singlevalued map. An application to boundary value problems for differential equations in Banach spaces is given.},
author = {Gabor, Dorota},
journal = {Annales Polonici Mathematici},
keywords = {condensing map; Fredholm operator; boundary value problem in Banach spaces; fixed point index; coincidence points; coincidence point; boundary value problem; upper semicontinuous; ultimately compact maps; coincidence index; -th stable homotopy group of spheres},
language = {eng},
number = {2},
pages = {143-166},
title = {The coincidence index for fundamentally contractible multivalued maps with nonconvex values},
url = {http://eudml.org/doc/208391},
volume = {75},
year = {2000},
}

TY - JOUR
AU - Gabor, Dorota
TI - The coincidence index for fundamentally contractible multivalued maps with nonconvex values
JO - Annales Polonici Mathematici
PY - 2000
VL - 75
IS - 2
SP - 143
EP - 166
AB - We study a coincidence problem of the form A(x) ∈ ϕ (x), where A is a linear Fredholm operator with nonnegative index between Banach spaces and ϕ is a multivalued A-fundamentally contractible map (in particular, it is not necessarily compact). The main tool is a coincidence index, which becomes the well known Leray-Schauder fixed point index when A=id and ϕ is a compact singlevalued map. An application to boundary value problems for differential equations in Banach spaces is given.
LA - eng
KW - condensing map; Fredholm operator; boundary value problem in Banach spaces; fixed point index; coincidence points; coincidence point; boundary value problem; upper semicontinuous; ultimately compact maps; coincidence index; -th stable homotopy group of spheres
UR - http://eudml.org/doc/208391
ER -

References

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