The coincidence index for fundamentally contractible multivalued maps with nonconvex values
Volume 75 / 2000
Annales Polonici Mathematici 75 (2000), 143-166
DOI: 10.4064/ap-75-2-143-166
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.
