Accepted for publication in JNEEA: Ms #2404251

Asymptotically almost periodic solutions of abstract nonlinear Volterra equations

Marko Kostić

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

Received on April 25, 2024, revised on June 5, 2024
Accepted on June 5, 2024

Communicated by Gaston M. N'Guérékata

Abstract.  In this note, we analyze the existence and uniqueness of asymptotically almost periodic solutions for a class of the abstract nonlinear Volterra integro-differential equations with Lipschitz continuous operators. We also provide the basic results about the class of mild (a, k, C, B)-regularized resolvent families in the nonlinear setting and the well-posedness of abstract nonlinear Volterra inclusions.
Keywords: Asymptotically almost periodic functions, abstract nonlinear Volterra equations, (a, k, C, B)-regularized resolvent families.
2010 Mathematics Subject Classification:   42A75, 43A60, 47D99.

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