Existence result for the CR-Yamabe equation
In this note we will prove that the CR-Yamabe equation has infinitely many changing-sign solutions. The problem is variational but the associated functional does not satisfy the Palais-Smale compactness condition; by mean of a suitable group action we will define a subspace on which we can apply the...
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| Format: | Article |
| Language: | English |
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University of Bologna
2013-12-01
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| Series: | Bruno Pini Mathematical Analysis Seminar |
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| Online Access: | http://mathematicalanalysis.unibo.it/article/view/4017 |
| _version_ | 1819237503004049408 |
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| author | Vittorio Martino |
| author_facet | Vittorio Martino |
| author_sort | Vittorio Martino |
| collection | DOAJ |
| description | In this note we will prove that the CR-Yamabe equation has infinitely many changing-sign solutions. The problem is variational but the associated functional does not satisfy the Palais-Smale compactness condition; by mean of a suitable group action we will define a subspace on which we can apply the minimax argument of Ambrosetti-Rabinowitz. The result solves a question left open from the classification results of positive solutions by Jerison-Lee in the '80s. |
| first_indexed | 2024-12-23T13:21:22Z |
| format | Article |
| id | doaj.art-c862e4d5504e40cda0252d0bdc7af9da |
| institution | Directory Open Access Journal |
| issn | 2240-2829 |
| language | English |
| last_indexed | 2024-12-23T13:21:22Z |
| publishDate | 2013-12-01 |
| publisher | University of Bologna |
| record_format | Article |
| series | Bruno Pini Mathematical Analysis Seminar |
| spelling | doaj.art-c862e4d5504e40cda0252d0bdc7af9da2022-12-21T17:45:27ZengUniversity of BolognaBruno Pini Mathematical Analysis Seminar2240-28292013-12-014138463805Existence result for the CR-Yamabe equationVittorio Martino0Università di BolognaIn this note we will prove that the CR-Yamabe equation has infinitely many changing-sign solutions. The problem is variational but the associated functional does not satisfy the Palais-Smale compactness condition; by mean of a suitable group action we will define a subspace on which we can apply the minimax argument of Ambrosetti-Rabinowitz. The result solves a question left open from the classification results of positive solutions by Jerison-Lee in the '80s.http://mathematicalanalysis.unibo.it/article/view/4017Reeb vector fieldmountain-pass with symmetry |
| spellingShingle | Vittorio Martino Existence result for the CR-Yamabe equation Bruno Pini Mathematical Analysis Seminar Reeb vector field mountain-pass with symmetry |
| title | Existence result for the CR-Yamabe equation |
| title_full | Existence result for the CR-Yamabe equation |
| title_fullStr | Existence result for the CR-Yamabe equation |
| title_full_unstemmed | Existence result for the CR-Yamabe equation |
| title_short | Existence result for the CR-Yamabe equation |
| title_sort | existence result for the cr yamabe equation |
| topic | Reeb vector field mountain-pass with symmetry |
| url | http://mathematicalanalysis.unibo.it/article/view/4017 |
| work_keys_str_mv | AT vittoriomartino existenceresultforthecryamabeequation |