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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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
Keywords
- Coupled systems
- Double phase operator
- Existence and compactness results
- Multivalued convection term
- Nonlocal terms
- Obstacle effect