New discussion on global existence and attractivity of mild solutions for nonautonomous integrodifferential equations with state-dependent delay | ||
| Electronic Journal of Mathematical Analysis and Applications | ||
| Volume 11, Issue 2, July 2023, Pages 1-16 PDF (442.32 K) | ||
| Document Type: Reviews | ||
| DOI: 10.21608/ejmaa.2023.298748 | ||
| Authors | ||
| Mamadou Abdoul Diop* 1; Abdoul Aziz Ndiaye2; Mbarack Fall3; Mariama B Traore4 | ||
| 1Department of Mathematics Gaston Berger University | ||
| 2Department of Mathematics Gaston Berger University Senegal | ||
| 3Department of Mathematics Gaston Berger University Senegal | ||
| 4Department of Mathematics University of Bamako Mali | ||
| Abstract | ||
| As a result of their adaptability, the functional integrodifferential equations can be utilized in a wide variety of research and engineering subspecialties. In this paper, we study a class of functional integrodifferential equations with state-dependent delay in Banach spaces. We begin by investigating the global existence of mild solutions for this class of functional integrodifferential equations in Banach spaces. These equations have a state-dependent delay. The linear component of these equations is dependent on time and generates a linear evolution system. Using the resolvent operator theory in the sense of Grimmer's fixed point technique, a new set of sufficient conditions is formulated and proven for the global existence of mild solutions for the functional integrodifferential equation with state-dependent delay. In the next part of this investigation, we are going to look into the attractivity of mild solutions for functional integrodifferential equations with state-dependent delay. An example is given in order to illustrate the theory that was obtained. Some well-known results are generalized and extended. | ||
| Keywords | ||
| Evolution system; Resolvent operator; Infinte delay | ||
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