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

• Abdelhamid Bensalem ^[1] ; Abdelkrim Salim ^[2] ; Mouffak Benchohra ^[1]
  1. [1] Djillali Liabes University of Sidi Bel-Abbès
  2. [2] Hassiba Benbouali University of Chlef, Djillali Liabes University of Sidi Bel-Abbès
• Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 23, Nº 3, 2024
• Idioma: inglés
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• Resumen

  • 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 secondorder 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.