Controllability for nonlocal stochastic integrodifferential evolution equations with the lack of compactness. Issue 1 (3rd January 2022)

• Record Type: Journal Article
• Authors: Mahamat Barka, Ibrahim; Diop, Mamadou Abdoul; Ezzinbi, Khalil; Hassan Mahamat Hamit, Mahamat
• Is Part Of: Stochastic analysis and applications. Volume 40:Issue 1(2022)
• Page Start: 1
• Page End: 19
• Publication Date: 2022-01-03
• Subjects: Stochastic integrodifferential equations -- nonlocal condition -- resolvent operator -- measure of noncompactness -- Mönch fixed point Theorem -- controllability; 34F05 -- 47J35 -- 60H10; Stochastic analysis -- Periodicals; 519.2205
• DOI: 10.1080/07362994.2021.1881557
• Languages: English
• ISSNs: 0736-2994

Abstract

Abstract: In this work, we study the controllability of a class of stochastic integrodifferential equations with noncompact semigroups and nonlocal condition on Hilbert spaces.We suppose that the linear part admits a resolvent operator in the sense of Grimmer. Our main results are obtained by utilizing stochastic analysis theory, Kuratowski measure of noncompactness and Mönch fixed point Theorem. As a result, we obtain a generalization of a host of important results in the literature, without assuming the compactness of the resolvent operator. Finally, we provide an example to illustrate the efficiency of our results.