Electron. J. Differential Equations, Vol. 2019 (2019), No. 63, pp. 1-14.

Approximate controllability of quasilinear functional differential equations

Duranta Chutia, Rajib Haloi

Abstract:
In this article, we study the approximate controllability for quasilinear differential equations with deviating arguments in a Hilbert space. We establish sufficient conditions for the existence of a mild solution. We also obtain sufficient conditions for the controllability of quasilinear equations. Further, we use it to establish the approximate controllability for quasilinear differential equations with deviating arguments. We discuss examples in which the analytical results are applied.

Submitted July 30, 2018. Published May 8, 2019.
Math Subject Classifications: 35K59, 35K90, 93B05, 93C25.
Key Words: Quasilienar equations; approximate controllability; deviating arguments; Krasnoselskii's fixed point theorem.

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Duranta Chutia
Department of Mathematical Sciences
Tezpur University, Sonitpur
ASSAM, Pin- 784028, India
email: durantachutia123@gmail.com
Phone +913712-275511, Fax +913712-267006
Rajib Haloi
Department of Mathematical Sciences
Tezpur University, Sonitpur
ASSAM, Pin- 784028, India
email: rajib.haloi@gmail.com
Phone +913712-275511, Fax +913712-267006

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