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

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.

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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