Abstract
We consider a class of impulsive neutral second-order stochastic functional evolution equations. The Sadovskii fixed point theorem and the theory of strongly continuous cosine families of operators are used to investigate the sufficient conditions for the controllability of the system considered. An example is provided to illustrate our results.
Highlights
Controllability, as a fundamental concept of control theory, plays an important role both in stochastic and deterministic control problems
The Sadovskii fixed point theorem and the theory of strongly continuous cosine families of operators are used to investigate the sufficient conditions for the controllability of the system considered
With the help of fixed point theorem, Luo 8, 9 and Burton 10–13 have investigated the problem of controllability of the systems in Banach spaces
Summary
Controllability, as a fundamental concept of control theory, plays an important role both in stochastic and deterministic control problems. The second-order stochastic differential equations are the right. It is useful for engineers to model mechanical vibrations or charge on a capacitor or condenser subjected to white noise excitation by second-order stochastic differential equations. A useful tool for the study of abstract second-order equations is the fixed point theory and the theory of strongly continuous cosine families. The focus of this paper is the controllability of mild solutions for a class of impulsive neutral second-order stochastic evolution equations of the form:. The Sadovskii fixed point theorem and the theory of strongly continuous cosine families of operators are used to investigate the sufficient conditions for the controllability of the system considered. We will apply the Sadovskii fixed point theorem to investigate the controllability of mild solution of this class of equations.
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