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Existence of Solutions for Implicit Obstacle Problems of Fractional Laplacian Type Involving Set-Valued Operators

Author

Listed:
  • Dumitru Motreanu

    (Yulin Normal University
    Université de Perpignan)

  • Van Thien Nguyen

    (FPT University)

  • Shengda Zeng

    (Yulin Normal University
    Jagiellonian University in Krakow)

Abstract

The paper is devoted to a new kind of implicit obstacle problem given by a fractional Laplacian-type operator and a set-valued term, which is described by a generalized gradient. An existence theorem for the considered implicit obstacle problem is established, using a surjectivity theorem for set-valued mappings, Kluge’s fixed point principle and nonsmooth analysis.

Suggested Citation

  • Dumitru Motreanu & Van Thien Nguyen & Shengda Zeng, 2020. "Existence of Solutions for Implicit Obstacle Problems of Fractional Laplacian Type Involving Set-Valued Operators," Journal of Optimization Theory and Applications, Springer, vol. 187(2), pages 391-407, November.
    • Handle: RePEc:spr:joptap:v:187:y:2020:i:2:d:10.1007_s10957-020-01752-4
    DOI: 10.1007/s10957-020-01752-4
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    References listed on IDEAS

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    1. Li-Wen Zhou & Nan-Jing Huang, 2013. "Existence of Solutions for Vector Optimization on Hadamard Manifolds," Journal of Optimization Theory and Applications, Springer, vol. 157(1), pages 44-53, April.
    2. Yu Han & Nan-jing Huang, 2018. "Continuity and Convexity of a Nonlinear Scalarizing Function in Set Optimization Problems with Applications," Journal of Optimization Theory and Applications, Springer, vol. 177(3), pages 679-695, June.
    3. Senda Ounaies & Jean-Marc Bonnisseau & Souhail Chebbi, 2016. "Equilibrium of a production economy with noncompact attainable allocations set," Documents de travail du Centre d'Economie de la Sorbonne 16056r, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne, revised Oct 2017.
    4. Akhtar A. Khan & Dumitru Motreanu, 2018. "Inverse problems for quasi-variational inequalities," Journal of Global Optimization, Springer, vol. 70(2), pages 401-411, February.
    5. Akhtar A. Khan & Dumitru Motreanu, 2015. "Existence Theorems for Elliptic and Evolutionary Variational and Quasi-Variational Inequalities," Journal of Optimization Theory and Applications, Springer, vol. 167(3), pages 1136-1161, December.
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