Problem With Critical Sobolev Exponent and With Potential on SN
We consider the equation −divSNqx∇Snu=u2∗−1,u>0 in D’, u=0 on D′, where D′ is a geodesic ball with radius θ1, centered at the north pole, on SN, N≥4, and q is a positive continuous function. We prove the existence of solutions that depends only on the behavior of the potential q near its minima....
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Wiley
2024-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2024/3495135 |
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| _version_ | 1832543632142368768 |
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| author | Walid Refai Habib Yazidi |
| author_facet | Walid Refai Habib Yazidi |
| author_sort | Walid Refai |
| collection | DOAJ |
| description | We consider the equation −divSNqx∇Snu=u2∗−1,u>0 in D’, u=0 on D′, where D′ is a geodesic ball with radius θ1, centered at the north pole, on SN, N≥4, and q is a positive continuous function. We prove the existence of solutions that depends only on the behavior of the potential q near its minima. |
| format | Article |
| id | doaj-art-4a6a9f6f4b834553881fae3b7520a17c |
| institution | Kabale University |
| issn | 1687-0042 |
| language | English |
| publishDate | 2024-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-4a6a9f6f4b834553881fae3b7520a17c2025-02-03T11:37:23ZengWileyJournal of Applied Mathematics1687-00422024-01-01202410.1155/2024/3495135Problem With Critical Sobolev Exponent and With Potential on SNWalid Refai0Habib Yazidi1Department of mathematicsEcole Nationale Supérieure d’Ingénieurs de TunisWe consider the equation −divSNqx∇Snu=u2∗−1,u>0 in D’, u=0 on D′, where D′ is a geodesic ball with radius θ1, centered at the north pole, on SN, N≥4, and q is a positive continuous function. We prove the existence of solutions that depends only on the behavior of the potential q near its minima.http://dx.doi.org/10.1155/2024/3495135 |
| spellingShingle | Walid Refai Habib Yazidi Problem With Critical Sobolev Exponent and With Potential on SN Journal of Applied Mathematics |
| title | Problem With Critical Sobolev Exponent and With Potential on SN |
| title_full | Problem With Critical Sobolev Exponent and With Potential on SN |
| title_fullStr | Problem With Critical Sobolev Exponent and With Potential on SN |
| title_full_unstemmed | Problem With Critical Sobolev Exponent and With Potential on SN |
| title_short | Problem With Critical Sobolev Exponent and With Potential on SN |
| title_sort | problem with critical sobolev exponent and with potential on sn |
| url | http://dx.doi.org/10.1155/2024/3495135 |
| work_keys_str_mv | AT walidrefai problemwithcriticalsobolevexponentandwithpotentialonsn AT habibyazidi problemwithcriticalsobolevexponentandwithpotentialonsn |