Approximate controllability of the non-autonomous impulsive evolution equation with state-dependent delay in Banach spaces. (February 2021)

• Record Type: Journal Article
• Authors: Arora, S.; Mohan, Manil T.; Dabas, J.
• Is Part Of: Nonlinear analysis. Volume 39(2021)
• Publication Date: 2021-02
• Subjects: 34K06 -- 34A12 -- 37L05 -- 93B05; Approximate controllability -- Non-autonomous evolution equation -- State-dependent delay -- Fractional power operator -- Schauder's fixed point theorem; Nonlinear functional analysis -- Periodicals; Analyse fonctionnelle non linéaire -- Périodiques; Nonlinear functional analysis; Periodicals; 515.7248
• DOI: 10.1016/j.nahs.2020.100989
• Languages: English
• ISSNs: 1751-570X

Abstract

Abstract: In this paper, we consider the non-autonomous semilinear impulsive differential equations with state-dependent delay. The approximate controllability results of the first-order systems are obtained in a separable reflexive Banach space, which has a uniformly convex dual. In order to establish sufficient conditions of the approximate controllability of such a system, we have used the theory of linear evolution systems, properties of the resolvent operator and Schauder's fixed point theorem. Finally, we provide two concrete examples to validate our results. Highlights: Non-autonomous impulsive systems with state-dependent delay in Banach spaces. Sufficient conditions for approximate controllability. Extension of the work by Fu (2017) to separable reflexive Banach spaces.