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APPROXIMATE CONTROLLABILITY OF SECOND-ORDER STOCHASTIC DIFFERENTIAL EQUATIONS WITH IMPULSIVE EFFECTS

RATHINASAMY SAKTHIVEL

Department of Mathematics, Sungkyunkwan University, Suwon 440-746, South Korea

Corresponding author.

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YONG REN

School of Mathematics and Physics, University of Tasmania, Hobart, Tasmania 7001, Australia

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, and

N. I. MAHMUDOV

Department of Mathematics, Eastern Mediterranean University, Gazimagusa, Mersin 10, Turkey

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https://doi.org/10.1142/S0217984910023359Cited by:74 (Source: Crossref)

Abstract

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 the Holder'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.

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