Geodesic
The coincidence index for fundamentally contractible multivalued maps with nonconvex values
Annales Polonici Mathematici, Tome 75 (2000) no. 2, pp. 143-166

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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.
DOI : 10.4064/ap-75-2-143-166
Keywords: condensing map, Fredholm operator, boundary value problem in Banach spaces, fixed point index, coincidence points 
Dorota Gabor. The coincidence index for fundamentally contractible multivalued maps with nonconvex values. Annales Polonici Mathematici, Tome 75 (2000) no. 2, pp. 143-166. doi: 10.4064/ap-75-2-143-166
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