Critical elliptic systems involving multiple strongly–coupled Hardy–type terms
In this paper, we study the radially–symmetric and strictly–decreasing solutions to a system of critical elliptic equations in RN, which involves multiple critical nonlinearities and strongly–coupled Hardy– type terms. By the ODEs analysis methods, the asymptotic behaviors at the origin and infinity...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
De Gruyter
2019-07-01
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| Series: | Advances in Nonlinear Analysis |
| Subjects: | |
| Online Access: | https://doi.org/10.1515/anona-2020-0029 |
| _version_ | 1831591601849237504 |
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| author | Kang Dongsheng Liu Mengru Xu Liangshun |
| author_facet | Kang Dongsheng Liu Mengru Xu Liangshun |
| author_sort | Kang Dongsheng |
| collection | DOAJ |
| description | In this paper, we study the radially–symmetric and strictly–decreasing solutions to a system of critical elliptic equations in RN, which involves multiple critical nonlinearities and strongly–coupled Hardy– type terms. By the ODEs analysis methods, the asymptotic behaviors at the origin and infinity of solutions are proved. It is found that the singularities of u and v in the solution (u, v) are at the same level. Finally, an explicit form of least energy solutions is found under certain assumptions, which has all of the mentioned properties for the radial decreasing solutions. |
| first_indexed | 2024-12-18T01:27:11Z |
| format | Article |
| id | doaj.art-229496fd99154015acf2152259b74258 |
| institution | Directory Open Access Journal |
| issn | 2191-950X |
| language | English |
| last_indexed | 2024-12-18T01:27:11Z |
| publishDate | 2019-07-01 |
| publisher | De Gruyter |
| record_format | Article |
| series | Advances in Nonlinear Analysis |
| spelling | doaj.art-229496fd99154015acf2152259b742582022-12-21T21:25:41ZengDe GruyterAdvances in Nonlinear Analysis2191-950X2019-07-019186688110.1515/anona-2020-0029anona-2020-0029Critical elliptic systems involving multiple strongly–coupled Hardy–type termsKang Dongsheng0Liu Mengru1Xu Liangshun2School of Mathematics and Statistics, South–Central University for Nationalities, Wuhan 430074, Wuhan, ChinaSchool of Mathematics and Statistics, South–Central University for Nationalities, Wuhan 430074, Wuhan, ChinaSchool of Mathematics and Statistics, Central China Normal University, Wuhan 430079, Wuhan, ChinaIn this paper, we study the radially–symmetric and strictly–decreasing solutions to a system of critical elliptic equations in RN, which involves multiple critical nonlinearities and strongly–coupled Hardy– type terms. By the ODEs analysis methods, the asymptotic behaviors at the origin and infinity of solutions are proved. It is found that the singularities of u and v in the solution (u, v) are at the same level. Finally, an explicit form of least energy solutions is found under certain assumptions, which has all of the mentioned properties for the radial decreasing solutions.https://doi.org/10.1515/anona-2020-0029critical elliptic systemradial decreasing solutionasymptotic propertyhardy term35j4735j50 |
| spellingShingle | Kang Dongsheng Liu Mengru Xu Liangshun Critical elliptic systems involving multiple strongly–coupled Hardy–type terms Advances in Nonlinear Analysis critical elliptic system radial decreasing solution asymptotic property hardy term 35j47 35j50 |
| title | Critical elliptic systems involving multiple strongly–coupled Hardy–type terms |
| title_full | Critical elliptic systems involving multiple strongly–coupled Hardy–type terms |
| title_fullStr | Critical elliptic systems involving multiple strongly–coupled Hardy–type terms |
| title_full_unstemmed | Critical elliptic systems involving multiple strongly–coupled Hardy–type terms |
| title_short | Critical elliptic systems involving multiple strongly–coupled Hardy–type terms |
| title_sort | critical elliptic systems involving multiple strongly coupled hardy type terms |
| topic | critical elliptic system radial decreasing solution asymptotic property hardy term 35j47 35j50 |
| url | https://doi.org/10.1515/anona-2020-0029 |
| work_keys_str_mv | AT kangdongsheng criticalellipticsystemsinvolvingmultiplestronglycoupledhardytypeterms AT liumengru criticalellipticsystemsinvolvingmultiplestronglycoupledhardytypeterms AT xuliangshun criticalellipticsystemsinvolvingmultiplestronglycoupledhardytypeterms |