Exact controllability of mild solutions for a class of semilinear differential equations

Abstract

In this paper, by using the noncompact measure, we study the exact controllability of mild solutions for semilinear differential equation when the nonlocal term is Lipschitz continuous in general Banach space. Here, the regularity conditions of noncompact measure assumption in previous literature are not used, but instead we adopt the estimate of noncompact measure in different topological spaces, give the proper control function by the property of quotient space, and obtain the exact controllability of the differential equation. Therefore, our results can be regarded as a Generalization of the controllability field.

Keywords

Exact controllability / noncompact measure / semilinear differential equation / nonlocal condition

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