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A Class of Multivalued Quasi-Variational Inequalities with Applications

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Abstract

In this paper we deal with a class of nonlinear quasi-variational inequalities involving a set-valued map and a constraint set. First, we prove that the set of weak solutions of the inequality is nonempty, weakly compact and upper semicontinuous with respect to perturbations in the data. Then, the results are applied to a quasi variational-hemivariational inequality of elliptic kind. Finally, as an illustrative applications we examine a mathematical model of a nonsmooth static frictional unilateral contact problem for ideally locking materials in nonlinear elasticity.

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Funding

Project was supported by the European Union’s Horizon 2020 Research and Innovation Programme under the Marie Skłodowska-Curie grant agreement No. 823731 CONMECH, the Ministry of Science and Higher Education of Republic of Poland under Grants Nos. 4004/GGPJII/H2020/2018/0 and 440328/PnH2/2019, and the National Science Centre of Poland under Project No. 2021/41/B/ST1/01636.

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Authors and Affiliations

  1. College of Applied Mathematics, Chengdu University of Information Technology, Chengdu, 610225, Sichuan Province, People’s Republic of China

    Stanislaw Migórski

  2. School of Science, Guangxi University of Science and Technology, Liuzhou, 545006, Guangxi Province, People’s Republic of China

    Yunru Bai

  3. Chair of Optimization and Control, Jagiellonian University, ul. Lojasiewicza 6, 30348, Krakow, Poland

    Stanislaw Migórski

  4. Department of Applied Mathematics, Faculty of Computer Science and Telecommunications, Krakow University of Technology, ul. Warszawska 24, 31155, Krakow, Poland

    Sylwia Dudek

Authors
  1. Stanislaw Migórski
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  2. Yunru Bai
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  3. Sylwia Dudek
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Contributions

All authors contributed to the study conception. Material preparation, data collection and analysis were performed by all authors. The first draft of the manuscript was written by Stanislaw Migorski and all authors commented on previous versions of the manuscript. All authors read and approved the final manuscript. Yunru Bai is the corresponding author.

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Correspondence to Yunru Bai.

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Project was supported by the European Union’s Horizon 2020 Research and Innovation Programme under the Marie Skłodowska-Curie grant agreement No. 823731 CONMECH, the Ministry of Science and Higher Education of Republic of Poland under Grants Nos. 4004/GGPJII/H2020/2018/0 and 440328/PnH2/2019, and the National Science Centre of Poland under Project No. 2021/41/B/ST1/01636.

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Migórski, S., Bai, Y. & Dudek, S. A Class of Multivalued Quasi-Variational Inequalities with Applications. Appl Math Optim 87, 32 (2023). https://doi.org/10.1007/s00245-022-09941-5

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  • DOI: https://doi.org/10.1007/s00245-022-09941-5

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