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Mixed Equilibrium Problems and Anti-periodic Solutions for Nonlinear Evolution Equations

Author

Listed:
  • Ouayl Chadli

    (Ibn Zohr University)

  • Qamrul Hasan Ansari

    (Aligarh Muslim University
    King Fahd University of Petroleum and Minerals)

  • Jen-Chih Yao

    (China Medical University
    King Abdulaziz University)

Abstract

By using some new developments in the theory of equilibrium problems, we study the existence of anti-periodic solutions for nonlinear evolution equations associated with time-dependent pseudomonotone and quasimonotone operators in the topological sense. More precisely, we establish new existence results for mixed equilibrium problems associated with pseudomonotone and quasimonotone bifunctions in the topological sense. The results obtained are therefore applied to study the existence of anti-periodic solutions for nonlinear evolution equations in the setting of reflexive Banach spaces. This new approach leads us to improve and unify most of the recent results obtained in this direction.

Suggested Citation

  • Ouayl Chadli & Qamrul Hasan Ansari & Jen-Chih Yao, 2016. "Mixed Equilibrium Problems and Anti-periodic Solutions for Nonlinear Evolution Equations," Journal of Optimization Theory and Applications, Springer, vol. 168(2), pages 410-440, February.
    • Handle: RePEc:spr:joptap:v:168:y:2016:i:2:d:10.1007_s10957-015-0707-y
    DOI: 10.1007/s10957-015-0707-y
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    References listed on IDEAS

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    1. O. Chadli & N.C. Wong & J.C. Yao, 2003. "Equilibrium Problems with Applications to Eigenvalue Problems," Journal of Optimization Theory and Applications, Springer, vol. 117(2), pages 245-266, May.
    2. M. Bianchi & R. Pini, 2005. "Coercivity Conditions for Equilibrium Problems," Journal of Optimization Theory and Applications, Springer, vol. 124(1), pages 79-92, January.
    3. Bigi, Giancarlo & Castellani, Marco & Pappalardo, Massimo & Passacantando, Mauro, 2013. "Existence and solution methods for equilibria," European Journal of Operational Research, Elsevier, vol. 227(1), pages 1-11.
    4. N. Hadjisavvas & S. Schaible, 1998. "From Scalar to Vector Equilibrium Problems in the Quasimonotone Case," Journal of Optimization Theory and Applications, Springer, vol. 96(2), pages 297-309, February.
    5. 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. Bijaya Kumar Sahu & Ouayl Chadli & Ram N. Mohapatra & Sabyasachi Pani, 2020. "Existence Results for Mixed Equilibrium Problems Involving Set-Valued Operators with Applications to Quasi-Hemivariational Inequalities," Journal of Optimization Theory and Applications, Springer, vol. 184(3), pages 810-823, March.
    2. 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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