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Optimal Mild Solutions for a Class of Nonlocal Multi-Valued Stochastic Delay Differential Equations

Author

Listed:
  • Zuomao Yan

    (Hexi University)

  • Li Han

    (Hexi University)

Abstract

In this paper, we introduce a new class of impulsive multi-valued stochastic delay differential equations with nonlocal conditions in separable Hilbert spaces. Using stochastic analysis, analytic semigroup, fractional powers of closed operators and suitable fixed point theorems, we prove the existence of optimal mild solutions for these systems in the $$\alpha $$ α -norm. An example is provided to illustrate the applicability of our results.

Suggested Citation

  • Zuomao Yan & Li Han, 2019. "Optimal Mild Solutions for a Class of Nonlocal Multi-Valued Stochastic Delay Differential Equations," Journal of Optimization Theory and Applications, Springer, vol. 181(3), pages 1053-1075, June.
    • Handle: RePEc:spr:joptap:v:181:y:2019:i:3:d:10.1007_s10957-019-01490-2
    DOI: 10.1007/s10957-019-01490-2
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    References listed on IDEAS

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    1. P. Balasubramaniam & P. Tamilalagan, 2017. "The Solvability and Optimal Controls for Impulsive Fractional Stochastic Integro-Differential Equations via Resolvent Operators," Journal of Optimization Theory and Applications, Springer, vol. 174(1), pages 139-155, July.
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