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Existence theorems of the variational-hemivariational inequalities

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  • Guo-ji Tang
  • Nan-jing Huang

Abstract

This paper is devoted to the existence of solutions for the variational-hemivariational inequalities in reflexive Banach spaces. Using the notion of the stable $${\phi}$$ -quasimonotonicity and the properties of Clarke’s generalized directional derivative and Clarke’s generalized gradient, some existence results of solutions are proved when the constrained set is nonempty, bounded (or unbounded), closed and convex. Moreover, a sufficient condition to the boundedness of the solution set and a necessary and sufficient condition to the existence of solutions are also derived. The results presented in this paper generalize and improve some known results. Copyright Springer Science+Business Media, LLC. 2013

Suggested Citation

  • Guo-ji Tang & Nan-jing Huang, 2013. "Existence theorems of the variational-hemivariational inequalities," Journal of Global Optimization, Springer, vol. 56(2), pages 605-622, June.
    • Handle: RePEc:spr:jglopt:v:56:y:2013:i:2:p:605-622
    DOI: 10.1007/s10898-012-9884-5
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    Cited by:

    1. Jinjie Liu & Xinmin Yang & Shengda Zeng & Yong Zhao, 2022. "Coupled Variational Inequalities: Existence, Stability and Optimal Control," Journal of Optimization Theory and Applications, Springer, vol. 193(1), pages 877-909, June.
    2. Shengda Zeng & Dumitru Motreanu & Akhtar A. Khan, 2022. "Evolutionary Quasi-Variational-Hemivariational Inequalities I: Existence and Optimal Control," Journal of Optimization Theory and Applications, Springer, vol. 193(1), pages 950-970, June.
    3. 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.

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