Some results on the approximate controllability of impulsive stochastic integro-differential equations with nonlocal conditions and state-dependent delay

Volume 15, Issue 4, pp 284--300 http://dx.doi.org/10.22436/jnsa.015.04.04

Publication Date: August 24, 2022 Submission Date: March 31, 2022 Revision Date: April 23, 2022 Accteptance Date: July 02, 2022

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Authors

M. Fall - UFR SAT Departement de Mathematiques, Universite Gaston Berger de Saint-Louis, B.P 234, Saint-Louis, Senegal. A. Mane - UFR SAT Departement de Mathematiques, Universite Gaston Berger de Saint-Louis, B.P 234, Saint-Louis, Senegal. B. Dehigbe - Institut de Math'ematiques et de Sciences Physiques , URMPM B.P. 613, Porto-Novo, Benin. M. A. Diop - UFR SAT Departement de Mathematiques, Universite Gaston Berger de Saint-Louis, B.P 234, Saint-Louis, Senegal. - UMMISCO UMI 209 IRD/UPMC, Bondy, France.

Abstract

This paper presents approximate controllability results for impulsive stochastic integro-differential systems with state-dependent delay in a Hilbert space. The use of the resolvent operator in the sense of Grimmer, as well as stochastic analysis techniques, yields a new set of results. Finally, an example is given to show how the theory that has been worked out can be put into practice.

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Keywords

• Impulsive stochastic integrodifferential equations
• state-dependent delay
• mild solution
• approximate controllability
• semigroup theory
• resolvent operator
• fixed point theorem
• nonlocal conditions

MSC

•  93B05
•  34A08
•  34A37
•  34F05

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