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Well-posedness for a Class of Variational–Hemivariational Inequalities with Perturbations

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Abstract

In this paper, we consider an extension of well-posedness for a minimization problem to a class of variational–hemivariational inequalities with perturbations. We establish some metric characterizations for the well-posed variational–hemivariational inequality and give some conditions under which the variational–hemivariational inequality is strongly well-posed in the generalized sense. Under some mild conditions, we also prove the equivalence between the well-posedness of variational–hemivariational inequality and the well-posedness of corresponding inclusion problem.

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Authors and Affiliations

  1. School of Mathematical Sciences, University of Electronic Science and Technology of China, Chengdu, Sichuan, 610054, P.R. China

    Yi-bin Xiao

  2. Department of Mathematics, Sichuan University, Chengdu, Sichuan, 610064, P.R. China

    Nan-jing Huang

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  1. Yi-bin Xiao
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  2. Nan-jing Huang
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Correspondence to Nan-jing Huang.

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Communicated by N. Hadjisavvas.

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Xiao, Yb., Huang, Nj. Well-posedness for a Class of Variational–Hemivariational Inequalities with Perturbations. J Optim Theory Appl 151, 33–51 (2011). https://doi.org/10.1007/s10957-011-9872-9

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  • DOI: https://doi.org/10.1007/s10957-011-9872-9

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