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Approximate controllability of second-order stochastic differential equations with impulsive effects. (English) Zbl 1211.93026
Summary: Many practical systems in physical and biological sciences have impulsive dynamical behaviors during the evolution process which can be modeled by impulsive differential equations. In this paper, the approximate controllability of nonlinear second-order stochastic infinite-dimensional dynamical systems with impulsive effects is considered. By using Hölder’s inequality, stochastic analysis and fixed point strategy, a new set of necessary and sufficient conditions are formulated which guarantees the approximate controllability of the nonlinear second-order stochastic system. The results are obtained under the assumption that the associated linear system is approximately controllable.

93E03General theory of stochastic systems
93C20Control systems governed by PDE
60H10Stochastic ordinary differential equations
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