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On the Existence of Solutions and Tikhonov Regularization of Hemivariational Inequality Problems

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Abstract

This paper is devoted to the existence of solution and Tikhonov regularization theory for a class of hemivariational inequalities. We give the existence of solutions for the class of hemivariational inequalities when the mappings satisfy the so-called hemivariational inequality property and a rather weak coercivity condition. The existence result allows us to deduce the Tikhonov regularization result. Our results generalize some results by He (Abstr. Appl. Anal. 2012, 172061, 2012) and others.

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Funding

The first author was partially supported by National Natural Science Foundations of China (11561008), Guangxi Natural Science Foundation (2014GXNSFAA118006), and Special Fund for Guangxi Bagui Scholars (WBS 2014-04). The second author was partially supported by National Natural Science Foundations of China (71471140). The third author was partially supported by the Natural Sciences and Engineering Research Council of Canada.

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Authors and Affiliations

  1. School of Mathematics and Statistics, Wuhan University, Wuhan, Hubei, 430072, People’s Republic of China

    Guo-ji Tang & Zhongping Wan

  2. School of Science, Guangxi University for Nationalities, Nanning, Guangxi, 530006, People’s Republic of China

    Guo-ji Tang

  3. Department of Mathematics, University of British Columbia, Kelowna, BC V1V 1V7, Canada

    Xianfu Wang

Authors
  1. Guo-ji Tang
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  2. Zhongping Wan
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  3. Xianfu Wang
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Correspondence to Xianfu Wang.

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Dedicated to Marco A. Lopez on the occasion of his 70th birthday.

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Tang, Gj., Wan, Z. & Wang, X. On the Existence of Solutions and Tikhonov Regularization of Hemivariational Inequality Problems. Vietnam J. Math. 48, 221–236 (2020). https://doi.org/10.1007/s10013-019-00362-6

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  • DOI: https://doi.org/10.1007/s10013-019-00362-6

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