# A Topological Fixed-Point Index Theory for Evolution Inclusions

### R. Bader

Technische Universität München, München Garching, Germany

## Abstract

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 ($U,V$)-approximation in the sense of Ben-El-Mechaiekh and Deguire. As applications we consider initial-value problems for nonlinear evolution inclusions of the type

$x_{′}(t)∈–A(t,x(t))+F(t,x(t))$

$∣x(0)=x_{0}$

where the operator $A$ satisfies various monotonicity assumptions and $F$ 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. 3–15

DOI 10.4171/ZAA/1001