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Existence and upper bound results for a class of nonlinear nonhomogeneous obstacle problems

Author

Listed:
  • Vo Minh Tam

    (Dong Thap University)

  • Shanli Liao

    (Yulin Normal University)

Abstract

This paper is devoted to the study of a new class of nonlinear obstacle problems involving nonhomogeneous partial differential operators and mixed boundary conditions. We provide the existence and uniqueness of the solution for the obstacle problem via applying a surjectivity theorem for set-valued mappings formulated by the sum of a set-valued pseudomonotone operator and a maximal monotone set-valued operator. Moreover, some upper bounds to the obstacle problem are established by using a regularized gap function through different norms.

Suggested Citation

  • Vo Minh Tam & Shanli Liao, 2024. "Existence and upper bound results for a class of nonlinear nonhomogeneous obstacle problems," Indian Journal of Pure and Applied Mathematics, Springer, vol. 55(1), pages 274-297, March.
    • Handle: RePEc:spr:indpam:v:55:y:2024:i:1:d:10.1007_s13226-022-00362-2
    DOI: 10.1007/s13226-022-00362-2
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    References listed on IDEAS

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    1. Jinxia Cen & Tahar Haddad & Van Thien Nguyen & Shengda Zeng, 2022. "Simultaneous distributed-boundary optimal control problems driven by nonlinear complementarity systems," Journal of Global Optimization, Springer, vol. 84(3), pages 783-805, November.
    2. Giancarlo Bigi & Mauro Passacantando, 2015. "D-gap functions and descent techniques for solving equilibrium problems," Journal of Global Optimization, Springer, vol. 62(1), pages 183-203, May.
    3. Suhel Ahmad Khan & Jia-Wei Chen, 2015. "Gap Functions and Error Bounds for Generalized Mixed Vector Equilibrium Problems," Journal of Optimization Theory and Applications, Springer, vol. 166(3), pages 767-776, September.
    4. Nguyen Van Hung & Vicente Novo & Vo Minh Tam, 2022. "Error bound analysis for vector equilibrium problems with partial order provided by a polyhedral cone," Journal of Global Optimization, Springer, vol. 82(1), pages 139-159, January.
    5. Khan, Suhel Ahmad & Chen, Jia-wei, 2015. "Gap function and global error bounds for generalized mixed quasi variational inequalities," Applied Mathematics and Computation, Elsevier, vol. 260(C), pages 71-81.
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