On the Variational Eigenvalues Which Are Not of Ljusternik-Schnirelmann Type
We discuss nonlinear homogeneous eigenvalue problems and the variational characterization of their eigenvalues. We focus on the Ljusternik-Schnirelmann method, present one possible alternative to this method and compare it with the Courant-Fischer minimax principle in the linear case. At the end we...
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| Format: | Article |
| Language: | English |
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Wiley
2012-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2012/434631 |
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| _version_ | 1832567251521241088 |
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| author | Pavel Drábek |
| author_facet | Pavel Drábek |
| author_sort | Pavel Drábek |
| collection | DOAJ |
| description | We discuss nonlinear homogeneous eigenvalue problems and the variational characterization of their eigenvalues. We focus on the Ljusternik-Schnirelmann method, present one possible alternative to this method and compare it with the Courant-Fischer minimax principle in the linear case. At the end we present a special nonlinear eigenvalue problem possessing an eigenvalue which allows the variational characterization but is not of Ljusternik-Schnirelmann type. |
| format | Article |
| id | doaj-art-a8a0622df34147d2b8730fab7c923456 |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2012-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-a8a0622df34147d2b8730fab7c9234562025-02-03T01:01:58ZengWileyAbstract and Applied Analysis1085-33751687-04092012-01-01201210.1155/2012/434631434631On the Variational Eigenvalues Which Are Not of Ljusternik-Schnirelmann TypePavel Drábek0Department of Mathematics and N.T.I.S., University of West Bohemia, Univerzitní 22, 306 14 Plzeň, Czech RepublicWe discuss nonlinear homogeneous eigenvalue problems and the variational characterization of their eigenvalues. We focus on the Ljusternik-Schnirelmann method, present one possible alternative to this method and compare it with the Courant-Fischer minimax principle in the linear case. At the end we present a special nonlinear eigenvalue problem possessing an eigenvalue which allows the variational characterization but is not of Ljusternik-Schnirelmann type.http://dx.doi.org/10.1155/2012/434631 |
| spellingShingle | Pavel Drábek On the Variational Eigenvalues Which Are Not of Ljusternik-Schnirelmann Type Abstract and Applied Analysis |
| title | On the Variational Eigenvalues Which Are Not of Ljusternik-Schnirelmann Type |
| title_full | On the Variational Eigenvalues Which Are Not of Ljusternik-Schnirelmann Type |
| title_fullStr | On the Variational Eigenvalues Which Are Not of Ljusternik-Schnirelmann Type |
| title_full_unstemmed | On the Variational Eigenvalues Which Are Not of Ljusternik-Schnirelmann Type |
| title_short | On the Variational Eigenvalues Which Are Not of Ljusternik-Schnirelmann Type |
| title_sort | on the variational eigenvalues which are not of ljusternik schnirelmann type |
| url | http://dx.doi.org/10.1155/2012/434631 |
| work_keys_str_mv | AT paveldrabek onthevariationaleigenvalueswhicharenotofljusternikschnirelmanntype |