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Applications of Equilibrium Problems to a Class of Noncoercive Variational Inequalities

Author

Listed:
  • O. Chadli

    (Ibn Zohr University)

  • Z. Liu

    (Central South University)

  • J. C. Yao

    (National Sun Yat-Sen University)

Abstract

In this paper, we are interested in the existence of solutions for a class of noncoercive variational inequalities involving a p-Laplacian type operator. Our approach is based essentially on equilibrium problems and arguments from recession analysis. Our results are of two types: the first is obtained in a monotone framework; the second is obtained without a monotonicity assumption.

Suggested Citation

  • O. Chadli & Z. Liu & J. C. Yao, 2007. "Applications of Equilibrium Problems to a Class of Noncoercive Variational Inequalities," Journal of Optimization Theory and Applications, Springer, vol. 132(1), pages 89-110, January.
    • Handle: RePEc:spr:joptap:v:132:y:2007:i:1:d:10.1007_s10957-006-9072-1
    DOI: 10.1007/s10957-006-9072-1
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    References listed on IDEAS

    as
    1. O. Chaldi & Z. Chbani & H. Riahi, 2000. "Equilibrium Problems with Generalized Monotone Bifunctions and Applications to Variational Inequalities," Journal of Optimization Theory and Applications, Springer, vol. 105(2), pages 299-323, May.
    2. K. L. Lin & D. P. Yang & J. C. Yao, 1997. "Generalized Vector Variational Inequalities," Journal of Optimization Theory and Applications, Springer, vol. 92(1), pages 117-125, January.
    3. O. Chadli & S. Schaible & J. C. Yao, 2004. "Regularized Equilibrium Problems with Application to Noncoercive Hemivariational Inequalities," Journal of Optimization Theory and Applications, Springer, vol. 121(3), pages 571-596, June.
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    Cited by:

    1. Adela Capătă, 2011. "Existence results for proper efficient solutions of vector equilibrium problems and applications," Journal of Global Optimization, Springer, vol. 51(4), pages 657-675, December.
    2. Nina Ovcharova & Joachim Gwinner, 2016. "Semicoercive Variational Inequalities: From Existence to Numerical Solution of Nonmonotone Contact Problems," Journal of Optimization Theory and Applications, Springer, vol. 171(2), pages 422-439, November.
    3. Ouayl Chadli & Joachim Gwinner & M. Zuhair Nashed, 2022. "Noncoercive Variational–Hemivariational Inequalities: Existence, Approximation by Double Regularization, and Application to Nonmonotone Contact Problems," Journal of Optimization Theory and Applications, Springer, vol. 193(1), pages 42-65, June.

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