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.
@article{bwmeta1.element.bwnjournal-article-apmv75z2p143bwm,
author = {Gabor, Dorota},
title = {The coincidence index for fundamentally contractible multivalued maps with nonconvex values},
journal = {Annales Polonici Mathematici},
volume = {75},
year = {2000},
pages = {143-166},
zbl = {0969.47041},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-apmv75z2p143bwm}
}
Gabor, Dorota. The coincidence index for fundamentally contractible multivalued maps with nonconvex values. Annales Polonici Mathematici, Tome 75 (2000) pp. 143-166. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-apmv75z2p143bwm/
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