Electron. J. Differential Equations, Vol. 2025 (2025), No. 54, pp. 1-18.
Optimal control and approximate controllability for second-order integro-differential equations with state-dependent delay and non-instantaneous impulses
Abdelhamid Bensalem, Abdelkrim Salim, Mouffak Benchohra, Gaston M. N'Guerekata
Abstract:
This article concerns the optimal control and the approximate controllability
for second order integro-differential equation with state-dependent delay
and non-instantaneous impulses. We first
establish the existence of mild solution for the control system.
Then, based on these results, we investigate the approximate controllability
and show the existence of optimal controls for Bolza problems by using the
resolvent family of linear operators, Monch's fixed point theorem, and
the resolvent condition. Finally, we give an example to illustrate the
effectiveness of the results.
Submitted March 3, 2025. Published May 26, 2025.
Math Subject Classifications: 93B05, 49N25, 45J05, 47H08, 34K45.
Key Words: Approximate controllability; optimal control; fixed point theorem;
infinite delay; second-order integrodifferential equation;
impulsive; measures of noncompactness; mild solution; resolvent operator.
DOI: 10.58997/ejde.2025.54
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Abdelhamid Bensalem
Laboratory of Mathematics
Djillali Liabes University of Sidi Bel-Abbès
P.O. Box 89, Sidi Bel-Abbès 22000, Algeria
email: bensalem.abdelhamid@yahoo.com
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Abdelkrim Salim
Laboratory of Mathematics
Djillali Liabes University of Sidi Bel-Abbès
P.O. Box 89, Sidi Bel-Abbès 22000, Algeria
email: salim.abdelkrim@yahoo.com
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Mouffak Benchohra
Laboratory of Mathematics
Djillali Liabes University of Sidi Bel-Abbès
P.O. Box 89, Sidi Bel-Abbès 22000, Algeria
email: benchohra@yahoo.com
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Gaston M. N'Guérékata
NEERLab, Department of Mathematics
Morgan State University
1700 E. Cold Spring Lane
Baltimore, MD 21252, USA
email: Gaston.NGuerekata@morgan.edu
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