Article Contents

2023, Volume 12, Issue 6: 1559-1576. Doi: 10.3934/eect.2023026

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Controllability results for second-order integro-differential equations with state-dependent delay

1.
Laboratory of Mathematics, Djillali Liabes University of Sidi Bel-Abbès, Algeria
2.
Faculty of Technology, Hassiba Benbouali University of Chlef, Algeria
3.
Departamento de Estatistica, Análise Matemática e Optimización, CITMAga, Universidade de Santiago de Compostela, Spain

^*Corresponding author: Abdelkrim Salim
^*Corresponding author: Abdelkrim Salim

Dedicated to Johnny Henderson for his retirement

Received: January 2023

Revised: April 2023

Early access: May 2023

Published: December 2023

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Abstract

The purpose of this study is to use resolvent operators to investigate the existence and the controllability of a mild solution to a second-order semilinear integro-differential problem. To construct our criterion, we use a fixed point theorem in conjunction with measures of noncompactness. A practical example is used to illustrate the obtained results.

Keywords:

Mild solution,
approximate controllability,
complete controllability,
fixed point theorem,
infinite delay,
second-order integro-differential equation,
measures of noncompactness,
resolvent operator,
state-dependent delay.

Mathematics Subject Classification: Primary: 93B05, 47H10, 45J05; Secondary: 47H08, 35D30, 47B40, 34K45.

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References

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