Solution Sets for Second-Order Integro-Differential Inclusions with Infinite Delay

The primary focus of this paper is threefold: first, to investigate the existence of mild solutions; second, to analyze the topological and geometrical structure of the solution sets; and third, to determine the continuous dependence of the solution for second-order semilinear integro-differential i...

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Bibliographic Details
Published in:Qualitative theory of dynamical systems 2024-07, Vol.23 (3), Article 144
Main Authors: Bensalem, Abdelhamid, Salim, Abdelkrim, Benchohra, Mouffak
Format: Article
Language:English
Subjects:
Difference and Functional Equations
Dynamical Systems and Ergodic Theory
Fixed points (mathematics)
Inclusions
Mathematics
Mathematics and Statistics
Operators (mathematics)
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Summary:The primary focus of this paper is threefold: first, to investigate the existence of mild solutions; second, to analyze the topological and geometrical structure of the solution sets; and third, to determine the continuous dependence of the solution for second-order semilinear integro-differential inclusion. In this study, we employ Bohnenblust–Karlin’s fixed point theorem in conjunction with the theory of resolvent operators, as presented by Grimmer. An illustrative example is employed to showcase the achieved outcomes.
ISSN:1575-5460
1662-3592
DOI:10.1007/s12346-024-01003-1