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Approximate controllability of nonlinear stochastic impulsive integrodifferential systems in hilbert spaces

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  • Subalakshmi, R.
  • Balachandran, K.

Abstract

Many practical systems in physical and biological sciences have impulsive dynamical behaviours during the evolution process which can be modeled by impulsive differential equations. This paper studies the approximate controllability properties of nonlinear stochastic impulsive integrodifferential and neutral functional stochastic impulsive integrodifferential equations in Hilbert spaces. Assuming the conditions for the approximate controllability of these linear systems we obtain the sufficient conditions for the approximate controllability of these associated nonlinear stochastic impulsive integrodifferential systems in Hilbert spaces. The results are obtained by using the Nussbaum fixed-point theorem. Finally, two examples are presented to illustrate the utility of the proposed result.

Suggested Citation

  • Subalakshmi, R. & Balachandran, K., 2009. "Approximate controllability of nonlinear stochastic impulsive integrodifferential systems in hilbert spaces," Chaos, Solitons & Fractals, Elsevier, vol. 42(4), pages 2035-2046.
    • Handle: RePEc:eee:chsofr:v:42:y:2009:i:4:p:2035-2046
    DOI: 10.1016/j.chaos.2009.03.166
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    References listed on IDEAS

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    1. Gao, Caixia & Li, Kezan & Feng, Enmin & Xiu, Zhilong, 2006. "Nonlinear impulsive system of fed-batch culture in fermentative production and its properties," Chaos, Solitons & Fractals, Elsevier, vol. 28(1), pages 271-277.
    2. Chang, Yong-Kui, 2007. "Controllability of impulsive functional differential systems with infinite delay in Banach spaces," Chaos, Solitons & Fractals, Elsevier, vol. 33(5), pages 1601-1609.
    3. Li, Meili & Wang, Miansen & Zhang, Fengqin, 2006. "Controllability of impulsive functional differential systems in Banach spaces," Chaos, Solitons & Fractals, Elsevier, vol. 29(1), pages 175-181.
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    1. Feng, Lichao & Liu, Lei & Wu, Zhihui & Liu, Qiumei, 2021. "Stability analysis for nonlinear Markov jump neutral stochastic functional differential systems," Applied Mathematics and Computation, Elsevier, vol. 394(C).

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