Approximate controllability of the non-autonomous impulsive evolution equation with state-dependent delay in Banach spaces |
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Institution: | 1. PG & Research Department of Mathematics, Kongunadu Arts and Science College, Coimbatore, Tamil Nadu 641029, India;2. Department of Mathematics, Sri Eshwar College of Engineering, Coimbatore, Tamil Nadu 641202, India;3. Instituto de Matemáticas, Facultade de Matemáticas, Universidade de Santiago de Compostela, Santiago de Compostela 15782, Spain |
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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. |
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Keywords: | Approximate controllability Non-autonomous evolution equation State-dependent delay Fractional power operator Schauder’s fixed point theorem |
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