In the paper we construct a topological fixed-point theory for a class of set-valued maps which appears in natural way in boundary value problems for differential inclusions. Our construction is based upon the notion of ()-approximation in the sense of Ben-El-Mechaiekh and Deguire. As applications we consider initial-value problems for nonlinear evolution inclusions of the type
where the operator satisfies various monotonicity assumptions and is an upper semicontinuous set-valued perturbation.
Cite this article
R. Bader, A Topological Fixed-Point Index Theory for Evolution Inclusions. Z. Anal. Anwend. 20 (2001), no. 1, pp. 3–15DOI 10.4171/ZAA/1001