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Approximate controllability for stochastic evolution inclusions of Clarke’s subdifferential type

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  • Lu, Liang
  • Liu, Zhenhai
  • Bin, Maojun

Abstract

In this paper, we deal with the approximate controllability of stochastic evolution inclusions of Clarke’s subdifferential type. Firstly, by using stochastic analysis, nonsmooth analysis, theory of operator semigroups and fixed point theorems of multivalued maps, we show the existence of mild solutions for the stochastic evolution inclusions. Then we provide a sufficient condition to guarantee the approximate controllability of the stochastic evolution inclusions. Actually, our results cover a broader class of inclusion problems involving time depending operators. Finally, an example is included to illustrate the applicability of the main results.

Suggested Citation

  • Lu, Liang & Liu, Zhenhai & Bin, Maojun, 2016. "Approximate controllability for stochastic evolution inclusions of Clarke’s subdifferential type," Applied Mathematics and Computation, Elsevier, vol. 286(C), pages 201-212.
    • Handle: RePEc:eee:apmaco:v:286:y:2016:i:c:p:201-212
    DOI: 10.1016/j.amc.2016.04.020
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    References listed on IDEAS

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    1. Balasubramaniam, P. & Tamilalagan, P., 2015. "Approximate controllability of a class of fractional neutral stochastic integro-differential inclusions with infinite delay by using Mainardi’s function," Applied Mathematics and Computation, Elsevier, vol. 256(C), pages 232-246.
    2. Arora, Urvashi & Sukavanam, N., 2015. "Approximate controllability of second order semilinear stochastic system with nonlocal conditions," Applied Mathematics and Computation, Elsevier, vol. 258(C), pages 111-119.
    3. Liu, Zhenhai & Zeng, Biao, 2015. "Existence and controllability for fractional evolution inclusions of Clarke’s subdifferential type," Applied Mathematics and Computation, Elsevier, vol. 257(C), pages 178-189.
    4. Wang, JinRong, 2015. "Approximate mild solutions of fractional stochastic evolution equations in Hilbert spaces," Applied Mathematics and Computation, Elsevier, vol. 256(C), pages 315-323.
    5. Lu, Liang & Liu, Zhenhai, 2015. "Existence and controllability results for stochastic fractional evolution hemivariational inequalities," Applied Mathematics and Computation, Elsevier, vol. 268(C), pages 1164-1176.
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    Cited by:

    1. Kavitha, K. & Vijayakumar, V. & Shukla, Anurag & Nisar, Kottakkaran Sooppy & Udhayakumar, R., 2021. "Results on approximate controllability of Sobolev-type fractional neutral differential inclusions of Clarke subdifferential type," Chaos, Solitons & Fractals, Elsevier, vol. 151(C).
    2. Durga, N. & Muthukumar, P., 2019. "Existence and exponential behavior of multi-valued nonlinear fractional stochastic integro-differential equations with Poisson jumps of Clarke’s subdifferential type," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 155(C), pages 347-359.
    3. Upadhyay, Anjali & Kumar, Surendra, 2023. "The exponential nature and solvability of stochastic multi-term fractional differential inclusions with Clarke’s subdifferential," Chaos, Solitons & Fractals, Elsevier, vol. 168(C).

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