Abstract
The controllability of semilinear stochastic delay evolution equations is studied by using a stochastic version of the well‐known Banach fixed point theorem and semigroup theory. An application to stochastic partial differential equations is given.
Highlights
The fixed point technique is widely used as a tool to study the controllability of nonlinear systems in finite- and infinite-dimensional Banach spaces, see the early survey paper by Balachandran and Dauer [5]
Anichini [2] and Yamamoto [14] studied the controllability of the classical nonlinear system by means of Schaefer’s theorem and Schauder’s theorem, respectively
Several authors have extended the finite-dimensional controllability results to infinite-dimensional controllability results represented by evolution equations with bounded and unbounded operators in Banach spaces
Summary
The fixed point technique is widely used as a tool to study the controllability of nonlinear systems in finite- and infinite-dimensional Banach spaces, see the early survey paper by Balachandran and Dauer [5]. Several authors have extended the finite-dimensional controllability results to infinite-dimensional controllability results represented by evolution equations with bounded and unbounded operators in Banach spaces (e.g., see Balachandran et al [4] and Dauer and Balasubramaniam [7]).
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