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. | |