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The relative Lefschetz and Nielsenfixed-point theorems are generalized for compact absorbingcontractions on ANR-spaces and nilmanifolds. The nontrivialLefschetz number implies the existence of a fixed-point in theclosure of the complementary domain. The relative Nielsen numbersimprove the lower estimate of the number of coincidences on thetotal space or indicate the location of fixed-points on thecomplement. Nontrivial applications of these topologicalinvariants (under homotopy) are given to admissible semi-flowsand differential inclusions.

Relative versions of the multivalued Lefschetz and Nielsen theorems and their application to admissible semi-flows