JournalszaaVol. 20, No. 1pp. 3–15

A Topological Fixed-Point Index Theory for Evolution Inclusions

  • R. Bader

    Technische Universität München, München Garching, Germany
A Topological Fixed-Point Index Theory for Evolution Inclusions cover
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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,VU, 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'(t) \in –A(t,x(t)) + F(t, x(t))
x(0)=x0|x(0) = x_0

where the operator AA satisfies various monotonicity assumptions and FF 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