Nielsen number and differential equations
<p/> <p>In reply to a problem of Jean Leray (application of the Nielsen theory to differential equations), two main approaches are presented. The first is via Poincaré's translation operator, while the second one is based on the Hammerstein-type solution operator. The appli...
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| Format: | Article |
| Language: | English |
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SpringerOpen
2005-01-01
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| Series: | Fixed Point Theory and Applications |
| Online Access: | http://www.fixedpointtheoryandapplications.com/content/2005/268678 |
| _version_ | 1818999308346720256 |
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| author | Andres Jan |
| author_facet | Andres Jan |
| author_sort | Andres Jan |
| collection | DOAJ |
| description | <p/> <p>In reply to a problem of Jean Leray (application of the Nielsen theory to differential equations), two main approaches are presented. The first is via Poincaré's translation operator, while the second one is based on the Hammerstein-type solution operator. The applicability of various Nielsen theories is discussed with respect to several sorts of differential equations and inclusions. Links with the Sharkovskii-like theorems (a finite number of periodic solutions imply infinitely many subharmonics) are indicated, jointly with some further consequences like the nontrivial <inline-formula><graphic file="1687-1812-2005-268678-i1.gif"/></inline-formula>-structure of solutions of initial value problems. Some illustrating examples are supplied and open problems are formulated.</p> |
| first_indexed | 2024-12-20T22:15:21Z |
| format | Article |
| id | doaj.art-1c29beb587d149229531673cd78c1d97 |
| institution | Directory Open Access Journal |
| issn | 1687-1820 1687-1812 |
| language | English |
| last_indexed | 2024-12-20T22:15:21Z |
| publishDate | 2005-01-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Fixed Point Theory and Applications |
| spelling | doaj.art-1c29beb587d149229531673cd78c1d972022-12-21T19:25:03ZengSpringerOpenFixed Point Theory and Applications1687-18201687-18122005-01-0120052268678Nielsen number and differential equationsAndres Jan<p/> <p>In reply to a problem of Jean Leray (application of the Nielsen theory to differential equations), two main approaches are presented. The first is via Poincaré's translation operator, while the second one is based on the Hammerstein-type solution operator. The applicability of various Nielsen theories is discussed with respect to several sorts of differential equations and inclusions. Links with the Sharkovskii-like theorems (a finite number of periodic solutions imply infinitely many subharmonics) are indicated, jointly with some further consequences like the nontrivial <inline-formula><graphic file="1687-1812-2005-268678-i1.gif"/></inline-formula>-structure of solutions of initial value problems. Some illustrating examples are supplied and open problems are formulated.</p>http://www.fixedpointtheoryandapplications.com/content/2005/268678 |
| spellingShingle | Andres Jan Nielsen number and differential equations Fixed Point Theory and Applications |
| title | Nielsen number and differential equations |
| title_full | Nielsen number and differential equations |
| title_fullStr | Nielsen number and differential equations |
| title_full_unstemmed | Nielsen number and differential equations |
| title_short | Nielsen number and differential equations |
| title_sort | nielsen number and differential equations |
| url | http://www.fixedpointtheoryandapplications.com/content/2005/268678 |
| work_keys_str_mv | AT andresjan nielsennumberanddifferentialequations |