Towards a Morse theory on Banach spaces via ultrafunctions
Morse Theory on Banach spaces would be a useful tool in nonlinear analysis but its development is hindered by many technical problems. In this paper we present an approach based on a new notion of generalized functions called “ultrafunctions” which solves some of the technical questions involved....
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Emerald Publishing
2015-07-01
|
| Series: | Arab Journal of Mathematical Sciences |
| Subjects: | |
| Online Access: | http://www.sciencedirect.com/science/article/pii/S1319516615000183 |
| _version_ | 1830178497428979712 |
|---|---|
| author | Vieri Benci Isaia Nisoli |
| author_facet | Vieri Benci Isaia Nisoli |
| author_sort | Vieri Benci |
| collection | DOAJ |
| description | Morse Theory on Banach spaces would be a useful tool in nonlinear analysis but its development is hindered by many technical problems. In this paper we present an approach based on a new notion of generalized functions called “ultrafunctions” which solves some of the technical questions involved. |
| first_indexed | 2024-12-17T19:42:28Z |
| format | Article |
| id | doaj.art-63a78f88ed5346a8b9f68b01febe28b4 |
| institution | Directory Open Access Journal |
| issn | 1319-5166 |
| language | English |
| last_indexed | 2024-12-17T19:42:28Z |
| publishDate | 2015-07-01 |
| publisher | Emerald Publishing |
| record_format | Article |
| series | Arab Journal of Mathematical Sciences |
| spelling | doaj.art-63a78f88ed5346a8b9f68b01febe28b42022-12-21T21:34:57ZengEmerald PublishingArab Journal of Mathematical Sciences1319-51662015-07-0121214415810.1016/j.ajmsc.2015.05.004Towards a Morse theory on Banach spaces via ultrafunctionsVieri Benci0Isaia Nisoli1Dipartimento di Matematica, Università degli Studi di Pisa, Via F. Buonarroti 1/c, 56127 Pisa, ItalyInstituto de Matemática - UFRJ Av. Athos da Silveira Ramos 149, Centro de Tecnologia - Bloco C Cidade Universitária - Ilha do Fundão, Caixa Postal 68530 21941-909 Rio de Janeiro - RJ, BrazilMorse Theory on Banach spaces would be a useful tool in nonlinear analysis but its development is hindered by many technical problems. In this paper we present an approach based on a new notion of generalized functions called “ultrafunctions” which solves some of the technical questions involved.http://www.sciencedirect.com/science/article/pii/S1319516615000183Non Archimedean MathematicsNon Standard AnalysisUltrafunctionsGeneralized solutionsCritical pointMorse indexMorse theory |
| spellingShingle | Vieri Benci Isaia Nisoli Towards a Morse theory on Banach spaces via ultrafunctions Arab Journal of Mathematical Sciences Non Archimedean Mathematics Non Standard Analysis Ultrafunctions Generalized solutions Critical point Morse index Morse theory |
| title | Towards a Morse theory on Banach spaces via ultrafunctions |
| title_full | Towards a Morse theory on Banach spaces via ultrafunctions |
| title_fullStr | Towards a Morse theory on Banach spaces via ultrafunctions |
| title_full_unstemmed | Towards a Morse theory on Banach spaces via ultrafunctions |
| title_short | Towards a Morse theory on Banach spaces via ultrafunctions |
| title_sort | towards a morse theory on banach spaces via ultrafunctions |
| topic | Non Archimedean Mathematics Non Standard Analysis Ultrafunctions Generalized solutions Critical point Morse index Morse theory |
| url | http://www.sciencedirect.com/science/article/pii/S1319516615000183 |
| work_keys_str_mv | AT vieribenci towardsamorsetheoryonbanachspacesviaultrafunctions AT isaianisoli towardsamorsetheoryonbanachspacesviaultrafunctions |