From the Schauder fixed-point theorem to the applied multivalued Nielsen theory

Jan Andres, Lech Górniewicz

DOI: http://dx.doi.org/10.12775/TMNA.1999.030

Abstract


Starting from the famous Schauder fixed-point theorem, we present
some Lefschetz-like and Nielsen-like generalizations for certain
admissible (multivalued) self-maps on metric ANR-spaces. These
fixed-point principles are applied for obtaining the existence and
multiplicity results for boundary value problems.

Keywords


Fixed-point theorems; CAC-maps; ANR-spaces; Lefschetz number; Nielsen number; boundary value problems; differential systems; existence results; multiplicity results

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