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Zeitschrift für Analysis und ihre Anwendungen

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Volume 20, Issue 1, 2001, pp. 3–15
DOI: 10.4171/ZAA/1001

Published online: 2001-03-31

A Topological Fixed-Point Index Theory for Evolution Inclusions

R. Bader[1]

(1) Technische Universität München, München Garching, Germany

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 $$x'(t) \in –A(t,x(t)) + F(t, x(t))$$ $$|x(0) = x_0$$ where the operator $A$ satisfies various monotonicity assumptions and $F$ is an upper semicontinuous set-valued perturbation.

Keywords: Fixed-point index, ($U, V$)-approximation, evolution inclusions

Bader R.: A Topological Fixed-Point Index Theory for Evolution Inclusions. Z. Anal. Anwend. 20 (2001), 3-15. doi: 10.4171/ZAA/1001