Almost-periodicity problem as a fixed-point problem for evolution inclusions

Jan Andres, Alberto M. Bersani

DOI: http://dx.doi.org/10.12775/TMNA.2001.038

Abstract


Existence of almost-periodic solutions to quasi-linear evolution
inclusions under a Stepanov almost-periodic forcing is
nontraditionally examined by means of the Banach-like and the
Schauder-Tikhonov-like fixed-point theorems. These multivalued
fixed-point principles concern condensing operators in
almost-periodic function spaces or their suitable closed subsets.
The Bohr-Neugebauer-type theorem jointly with the Bochner
transform are employed, besides another, for this purpose.
Obstructions related to possible generalizations are discussed.

Keywords


Almost-periodic solutions; differential inclusions in Banach spaces; fixed-points; Stepanov almost-periodic forcing; Bohr-Neugebauer-type theorem; condensing operators; existence results

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