Three nontrivial solutions for Neumann problems resonant at any positive eigenvalue
We consider a semilinear Neumann problem with a parametric reaction which has a concave term and a perturbation which at ±∞ can be resonant with respect to any positive eigenvalue. Using variational methods based on the critical point theory and Morse theory, we show that there exists a critical par...
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| Format: | Article |
| Language: | English |
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Università degli Studi di Catania
2010-12-01
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| Series: | Le Matematiche |
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| Online Access: | http://www.dmi.unict.it/ojs/index.php/lematematiche/article/view/826 |
| _version_ | 1811206664915779584 |
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| author | Sophia Th. Kyritsi Nikolaus S. Papageorgiou |
| author_facet | Sophia Th. Kyritsi Nikolaus S. Papageorgiou |
| author_sort | Sophia Th. Kyritsi |
| collection | DOAJ |
| description | We consider a semilinear Neumann problem with a parametric reaction which has a concave term and a perturbation which at ±∞ can be resonant with respect to any positive eigenvalue. Using variational methods based on the critical point theory and Morse theory, we show that there exists a critical parameter value λ ∗ > 0 such that if λ ∈(0, λ ∗ ), then the problem has at least three nontrivial smooth solutions.<br /> |
| first_indexed | 2024-04-12T03:50:54Z |
| format | Article |
| id | doaj.art-a0799c64ffc4461a86fa4d631cfed142 |
| institution | Directory Open Access Journal |
| issn | 0373-3505 2037-5298 |
| language | English |
| last_indexed | 2024-04-12T03:50:54Z |
| publishDate | 2010-12-01 |
| publisher | Università degli Studi di Catania |
| record_format | Article |
| series | Le Matematiche |
| spelling | doaj.art-a0799c64ffc4461a86fa4d631cfed1422022-12-22T03:48:58ZengUniversità degli Studi di CataniaLe Matematiche0373-35052037-52982010-12-016527995762Three nontrivial solutions for Neumann problems resonant at any positive eigenvalueSophia Th. KyritsiNikolaus S. PapageorgiouWe consider a semilinear Neumann problem with a parametric reaction which has a concave term and a perturbation which at ±∞ can be resonant with respect to any positive eigenvalue. Using variational methods based on the critical point theory and Morse theory, we show that there exists a critical parameter value λ ∗ > 0 such that if λ ∈(0, λ ∗ ), then the problem has at least three nontrivial smooth solutions.<br />http://www.dmi.unict.it/ojs/index.php/lematematiche/article/view/826ResonanceConcave termUnique continuation propertyEkeland variational principleCritical groupsMorse relationNondegenerate critical point. |
| spellingShingle | Sophia Th. Kyritsi Nikolaus S. Papageorgiou Three nontrivial solutions for Neumann problems resonant at any positive eigenvalue Le Matematiche Resonance Concave term Unique continuation property Ekeland variational principle Critical groups Morse relation Nondegenerate critical point. |
| title | Three nontrivial solutions for Neumann problems resonant at any positive eigenvalue |
| title_full | Three nontrivial solutions for Neumann problems resonant at any positive eigenvalue |
| title_fullStr | Three nontrivial solutions for Neumann problems resonant at any positive eigenvalue |
| title_full_unstemmed | Three nontrivial solutions for Neumann problems resonant at any positive eigenvalue |
| title_short | Three nontrivial solutions for Neumann problems resonant at any positive eigenvalue |
| title_sort | three nontrivial solutions for neumann problems resonant at any positive eigenvalue |
| topic | Resonance Concave term Unique continuation property Ekeland variational principle Critical groups Morse relation Nondegenerate critical point. |
| url | http://www.dmi.unict.it/ojs/index.php/lematematiche/article/view/826 |
| work_keys_str_mv | AT sophiathkyritsi threenontrivialsolutionsforneumannproblemsresonantatanypositiveeigenvalue AT nikolausspapageorgiou threenontrivialsolutionsforneumannproblemsresonantatanypositiveeigenvalue |