Abstract
The aim of this article is to investigate the existence of mild solutions as well as approximate controllability of non-autonomous Sobolev type differential equations with the nonlocal condition. To prove our results, we will take the help of Krasnoselskii fixed point technique, evolution system and controllability of the corresponding linear system.
Highlights
We discuss the approximate controllability of nonlocal Sobolev type nonautonomous evolution equations in a separable Hilbert space X: d dt
Brill [4] first established the existence of solution for a semilinear Sobolev differential equation in a Banach space
Mahmudov [18] discussed the approximate controllability of autonomous fractional Sobolev type differential system in Banach space with the help of Schauder’s fixed point theorem
Summary
We discuss the approximate controllability of nonlocal Sobolev type nonautonomous evolution equations in a separable Hilbert space X:. Haloi et al [15] generalized the above results for nonautonomous differential equations with deviated arguments by the use of theory of analytic semigroup and Banach fixed point theorem. Hamdy [17] studied sufficient conditions for controllability of autonomous Sobolev type fractional integro-differential equations with the help of Schauder’s fixed point theorem and the theory of compact semigroup. Mahmudov [18] discussed the approximate controllability of autonomous fractional Sobolev type differential system in Banach space with the help of Schauder’s fixed point theorem. Haloi [19] established sufficient conditions for approximate controllability of non-autonomous nonlocal delay differential systems with deviating arguments by using theory of compact semigroup and Krasnoselskii fixed point theorem.
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