Coincidence of k-set contraction pairs
Let \(K(\bar U,C)\) be the family of all pairs \((p,q)\) such that \(F(p,q)\cap \partial U=\emptyset\) where \(p: \Gamma\to \bar U\) is a Vietoris map, \(q: \Gamma\to C\) is a compact map, \(\Gamma\) is a metric space, U is an open bounded subset of C, C is a closed convex subset of E and E is a fixed Banach space. The authors generalize the coincidence index defined by the second author [Bull. Acad. Polon. Sci., Sér. Sci. Math. Astron. Phys. 24, 245-252 (1976; Zbl 0334.55008)] to \(K(\bar U,C)\) and also to k-set contraction pairs. The definition uses a retraction \(r: E\to C\). The authors ask the question if the index depends on the choice of the retraction. They generalize the ''nonlinear alternative'' and the ''Leray-Schauder alternative'' theorems for k-set contraction pairs and give an application to a boundary value problem for differential inclusions.
scientific article; zbMATH DE number 3925791