High perturbations of Choquard equations with critical reaction and variable growth
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- by Youpei Zhang, Xianhua Tang and Vicenţiu D. Rădulescu PDF
- Proc. Amer. Math. Soc. 149 (2021), 3819-3835 Request permission
Abstract:
This paper deals with the mathematical analysis of solutions for a new class of Choquard equations. The main features of the problem studied in this paper are the following: (i) the equation is driven by a differential operator with variable exponent; (ii) the Choquard term contains a nonstandard potential with double variable growth; and (iii) the lack of compactness of the reaction, which is generated by a critical nonlinearity. The main result establishes the existence of infinitely many solutions in the case of high perturbations of the source term. The proof combines variational and analytic methods, including the Hardy-Littlewood-Sobolev inequality for variable exponents and the concentration-compactness principle for problems with variable growth.References
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Additional Information
- Youpei Zhang
- Affiliation: School of Mathematics and Statistics, Central South University, Changsha, Hunan 410083, People’s Republic of China; and Department of Mathematics, University of Craiova, 200585 Craiova, Romania
- Email: zhangypzn@163.com; youpei.zhang@inf.ucv.ro
- Xianhua Tang
- Affiliation: School of Mathematics and Statistics, Central South University, Changsha, Hunan 410083, People’s Republic of China
- Email: tangxh@mail.csu.edu.cn
- Vicenţiu D. Rădulescu
- Affiliation: Faculty of Applied Mathematics, AGH University of Science and Technology, al. Mickiewicza 30, 30-059 Kraków, Poland; Department of Mathematics, University of Craiova, 200585 Craiova, Romania; and Institute of Mathematics ‘Simion Stoilow’ of the Romanian Academy, PO Box 1-764, 014700 Bucharest, Romania
- MR Author ID: 143765
- ORCID: 0000-0003-4615-5537
- Email: radulescu@inf.ucv.ro
- Received by editor(s): September 22, 2020
- Received by editor(s) in revised form: December 6, 2020
- Published electronically: June 4, 2021
- Additional Notes: This research was partially supported by the National Natural Science Foundation of China (No. 11971485), the Fundamental Research Funds for the Central Universities of Central South University (No. 2019zzts211), and the Natural Science Foundation of Hunan Province (No. 2019JJ50146). This paper was completed while the first author was visiting University of Craiova (Romania) with the financial support of the China Scholarship Council (No. 201906370079)
The work of the first and third authors was supported by a grant of the Romanian Ministry of Research, Innovation and Digitization, CNCS/CCCDI-UEFISCDI, project number PCE 137/2021, within PNCDI III
The third author is the corresponding author. - Communicated by: Catherine Sulem
- © Copyright 2021 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 149 (2021), 3819-3835
- MSC (2020): Primary 35A15; Secondary 35J62, 58E50
- DOI: https://doi.org/10.1090/proc/15469
- MathSciNet review: 4291581