Nonexistence of positive solutions for the weighted higher-order elliptic system with Navier boundary condition
Abstract We establish a Liouville-type theorem for a weighted higher-order elliptic system in a wider exponent region described via a critical curve. We first establish a Liouville-type theorem to the involved integral system and then prove the equivalence between the two systems by using superharmo...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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SpringerOpen
2024-01-01
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| Series: | Boundary Value Problems |
| Subjects: | |
| Online Access: | https://doi.org/10.1186/s13661-024-01831-9 |
| _version_ | 1797276441173295104 |
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| author | Weiwei Zhao Xiaoling Shao Changhui Hu Zhiyu Cheng |
| author_facet | Weiwei Zhao Xiaoling Shao Changhui Hu Zhiyu Cheng |
| author_sort | Weiwei Zhao |
| collection | DOAJ |
| description | Abstract We establish a Liouville-type theorem for a weighted higher-order elliptic system in a wider exponent region described via a critical curve. We first establish a Liouville-type theorem to the involved integral system and then prove the equivalence between the two systems by using superharmonic properties of the differential systems. This improves the results in (Complex Var. Elliptic Equ. 5:1436–1450, 2013) and (Abstr. Appl. Anal. 2014:593210, 2014). |
| first_indexed | 2024-03-07T15:28:16Z |
| format | Article |
| id | doaj.art-ea11a85fc4d84bdbb676a66c1372674d |
| institution | Directory Open Access Journal |
| issn | 1687-2770 |
| language | English |
| last_indexed | 2024-03-07T15:28:16Z |
| publishDate | 2024-01-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Boundary Value Problems |
| spelling | doaj.art-ea11a85fc4d84bdbb676a66c1372674d2024-03-05T16:36:40ZengSpringerOpenBoundary Value Problems1687-27702024-01-012024111910.1186/s13661-024-01831-9Nonexistence of positive solutions for the weighted higher-order elliptic system with Navier boundary conditionWeiwei Zhao0Xiaoling Shao1Changhui Hu2Zhiyu Cheng3School of Mathematics and Statistics, Hainan UniversitySchool of Mathematics and Statistics, Hainan UniversitySchool of Cyberspace Security, School of Cryptology, Hainan UniversitySchool of Mathematics and Statistics, Hainan UniversityAbstract We establish a Liouville-type theorem for a weighted higher-order elliptic system in a wider exponent region described via a critical curve. We first establish a Liouville-type theorem to the involved integral system and then prove the equivalence between the two systems by using superharmonic properties of the differential systems. This improves the results in (Complex Var. Elliptic Equ. 5:1436–1450, 2013) and (Abstr. Appl. Anal. 2014:593210, 2014).https://doi.org/10.1186/s13661-024-01831-9Weighted higher-order elliptic systemLiouville-type theoremNavier boundary valueSuperharmonic property |
| spellingShingle | Weiwei Zhao Xiaoling Shao Changhui Hu Zhiyu Cheng Nonexistence of positive solutions for the weighted higher-order elliptic system with Navier boundary condition Boundary Value Problems Weighted higher-order elliptic system Liouville-type theorem Navier boundary value Superharmonic property |
| title | Nonexistence of positive solutions for the weighted higher-order elliptic system with Navier boundary condition |
| title_full | Nonexistence of positive solutions for the weighted higher-order elliptic system with Navier boundary condition |
| title_fullStr | Nonexistence of positive solutions for the weighted higher-order elliptic system with Navier boundary condition |
| title_full_unstemmed | Nonexistence of positive solutions for the weighted higher-order elliptic system with Navier boundary condition |
| title_short | Nonexistence of positive solutions for the weighted higher-order elliptic system with Navier boundary condition |
| title_sort | nonexistence of positive solutions for the weighted higher order elliptic system with navier boundary condition |
| topic | Weighted higher-order elliptic system Liouville-type theorem Navier boundary value Superharmonic property |
| url | https://doi.org/10.1186/s13661-024-01831-9 |
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