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....
| Published in: | Journal of Applied Mathematics |
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| Main Authors: | , |
| Format: | Article in Journal/Newspaper |
| Language: | English |
| Published: |
Wiley
2024
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| Subjects: | |
| Online Access: | https://doi.org/10.1155/2024/3495135 https://doaj.org/article/4a6a9f6f4b834553881fae3b7520a17c |
| Summary: | 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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