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Controllability of Impulsive Evolution Inclusions with Nonlocal Conditions

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  • M. Guo
  • X. Xue
  • R. Li

Abstract

In this paper, we examine controllability problems of evolution inclusions with nonlocal conditions. Using the set-valued and single-valued Mönch fixed-point theorem, we establish some sufficient conditions for the controllability under convex and nonconvex orientor fields respectively. Our approach is different from all previous approaches; we do not assume that the evolution system generates a compact semigroup; so, our method is applicable to a wide class of (impulsive) control systems and evolution inclusions in Banach spaces.

Suggested Citation

  • M. Guo & X. Xue & R. Li, 2004. "Controllability of Impulsive Evolution Inclusions with Nonlocal Conditions," Journal of Optimization Theory and Applications, Springer, vol. 120(2), pages 355-374, February.
    • Handle: RePEc:spr:joptap:v:120:y:2004:i:2:d:10.1023_b:jota.0000015688.53162.eb
    DOI: 10.1023/B:JOTA.0000015688.53162.eb
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    References listed on IDEAS

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    1. Papageorgiou, Nikolaos S., 1985. "On the theory of Banach space valued multifunctions. 1. Integration and conditional expectation," Journal of Multivariate Analysis, Elsevier, vol. 17(2), pages 185-206, October.
    2. Papageorgiou, Nikolaos S., 1985. "On the theory of Banach space valued multifunctions. 2. Set valued martingales and set valued measures," Journal of Multivariate Analysis, Elsevier, vol. 17(2), pages 207-227, October.
    3. M. Benchohra & S. K. Ntouyas, 2000. "Controllability of Second-Order Differential Inclusions in Banach Spaces with Nonlocal Conditions," Journal of Optimization Theory and Applications, Springer, vol. 107(3), pages 559-571, December.
    4. Hiai, Fumio & Umegaki, Hisaharu, 1977. "Integrals, conditional expectations, and martingales of multivalued functions," Journal of Multivariate Analysis, Elsevier, vol. 7(1), pages 149-182, March.
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