J. Nonl. Evol. Equ. Appl. 2022 (1), pp. 1-24, published on June 11, 2022:

Stepanov multi-dimensional almost automorphic type functions and applications

M. Kostic

Faculty of Technical Sciences, University of Novi Sad, Trg D. Obradovica 6, 21125 Novi Sad, Serbia

V. Kumar

Max-Planck Institute for Dynamics of Complex Technical Systems, Sandtorstr. 1, 39106 Magdeburg, Germany

M. Pinto

Departamento de Matematicas, Facultad de Ciencias, Universidad de Chile, Santiago de Chile, Chile

Received on January 20, 2022
Accepted on January 31, 2022

Communicated by Gaston M. N'Guérékata

Abstract.  The main purpose of this paper is to analyze various notions of Stepanov multi-dimensional almost automorphy in Lebesgue spaces with variable exponents. The introduced notion seems to be new even in the one-dimensional setting, with the exponent p(·) being constant. We provide some applications of our results to the abstract Volterra integro-differential equations.
Keywords:Stepanov multi-dimensional almost automorphic type functions, Stepanov multi-dimensional almost periodic type functions, Bochner transform, Lebesgue spaces with variable exponents, abstract Volterra integro-differential equations.
2010 Mathematics Subject Classification:   42A75, 43A60, 47D99..

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