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Coupled double phase obstacle systems involving nonlocal functions and multivalued convection terms

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Abstract

In this paper we study a new kind of coupled elliptic obstacle problems driven by double phase operators and with multivalued right-hand sides depending on the gradients of the solutions. Based on an abstract existence theorem for generalized mixed variational inequalities involving multivalued mappings due to Kenmochi (Hiroshima Math J 4:229–263, 1974), we prove the nonemptiness and compactness of the weak solution set of the coupled elliptic obstacle system.

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Acknowledgements

This project has received funding from the Natural Science Foundation of Guangxi Grant Nos. 2021GXNSFFA196004 and 2022AC21071, the NNSF of China Grant Nos. 12001478, 12026255, 12026256 and 11961074, the European Union’s Horizon 2020 Research and Innovation Programme under the Marie Sklodowska-Curie grant agreement No. 823731 CONMECH, National Science Center of Poland under Preludium Project No. 2017/25/N/ST1/00611, and the Startup Project of Doctor Scientific Research of Yulin Normal University No. G2020ZK07. It is also supported by the Ministry of Science and Higher Education of Republic of Poland under Grants Nos. 4004/GGPJII/H2020/2018/0 and 440328/PnH2/2019.

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Authors and Affiliations

  1. Guangxi Colleges and Universities Key Laboratory of Complex System Optimization and Big Data Processing, Yulin Normal University, Yulin, 537000, Guangxi, People’s Republic of China

    Yongjian Liu

  2. Department of Mathematics, FPT University, Education Zone, Hoa Lac High Tech Park, Km29 Thang Long Highway, Thach That Ward, Hanoi, Vietnam

    Van Thien Nguyen

  3. Institut für Mathematik, Technische Universität Berlin, Straße des 17. Juni 136, 10623, Berlin, Germany

    Patrick Winkert

  4. Department of Mathematics, Nanjing University, Nanjing, 210093, Jiangsu, People’s Republic of China

    Shengda Zeng

  5. Jagiellonian University in Krakow, Faculty of Mathematics and Computer Science, ul. Lojasiewicza 6, 30-348, Kraków, Poland

    Shengda Zeng

  6. Guangxi Colleges and Universities Key Laboratory of Complex System Optimization and Big Data Processing, Yulin Normal University, Yulin, 537000, Guangxi, People’s Republic of China

    Shengda Zeng

Authors
  1. Yongjian Liu
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  2. Van Thien Nguyen
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  3. Patrick Winkert
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  4. Shengda Zeng
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Correspondence to Shengda Zeng.

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Communicated by Michael Kunzinger.

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Liu, Y., Nguyen, V.T., Winkert, P. et al. Coupled double phase obstacle systems involving nonlocal functions and multivalued convection terms. Monatsh Math 202, 363–376 (2023). https://doi.org/10.1007/s00605-023-01825-2

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  • DOI: https://doi.org/10.1007/s00605-023-01825-2

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