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

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Abstract

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.

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Authors and Affiliations

  1. Laboratory of Mathematics, Djillali Liabes University of Sidi Bel-Abbès, P.O. Box 89, 22000, Sidi Bel-Abbès, Algeria

    Abdelhamid Bensalem, Abdelkrim Salim & Mouffak Benchohra

  2. Faculty of Technology, Hassiba Benbouali University of Chlef, P.O. Box 151, 02000, Chlef, Algeria

    Abdelkrim Salim

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  1. Abdelhamid Bensalem
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  3. Mouffak Benchohra
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Bensalem, A., Salim, A. & Benchohra, M. Solution Sets for Second-Order Integro-Differential Inclusions with Infinite Delay. Qual. Theory Dyn. Syst. 23, 144 (2024). https://doi.org/10.1007/s12346-024-01003-1

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