Lie Symmetries and Criticality of Semilinear Differential Systems
We discuss the notion of criticality of semilinear differential equations and systems, its relations to scaling transformations and the Noether approach to Pokhozhaev's identities. For this purpose we propose a definition for criticality based on the S. Lie symmetry theory. We show that this de...
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| Published in: | Symmetry, Integrability and Geometry: Methods and Applications |
|---|---|
| Date: | 2007 |
| Main Authors: | , |
| Format: | Article |
| Language: | English |
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Інститут математики НАН України
2007
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/147807 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | Lie Symmetries and Criticality of Semilinear Differential Systems / Y. Bozhkov, E. Mitidieri // Symmetry, Integrability and Geometry: Methods and Applications. — 2007. — Т. 3. — Бібліогр.: 39 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862673510648774656 |
|---|---|
| author | Bozhkov, Y. Mitidieri, E. |
| author_facet | Bozhkov, Y. Mitidieri, E. |
| citation_txt | Lie Symmetries and Criticality of Semilinear Differential Systems / Y. Bozhkov, E. Mitidieri // Symmetry, Integrability and Geometry: Methods and Applications. — 2007. — Т. 3. — Бібліогр.: 39 назв. — англ. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | We discuss the notion of criticality of semilinear differential equations and systems, its relations to scaling transformations and the Noether approach to Pokhozhaev's identities. For this purpose we propose a definition for criticality based on the S. Lie symmetry theory. We show that this definition is compatible with the well-known notion of critical exponent by considering various examples. We also review some related recent papers.
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| first_indexed | 2025-12-07T15:38:50Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-147807 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-12-07T15:38:50Z |
| publishDate | 2007 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Bozhkov, Y. Mitidieri, E. 2019-02-16T08:35:03Z 2019-02-16T08:35:03Z 2007 Lie Symmetries and Criticality of Semilinear Differential Systems / Y. Bozhkov, E. Mitidieri // Symmetry, Integrability and Geometry: Methods and Applications. — 2007. — Т. 3. — Бібліогр.: 39 назв. — англ. 1815-0659 2000 Mathematics Subject Classification: 35J50; 35J20; 35J60; 35L70 https://nasplib.isofts.kiev.ua/handle/123456789/147807 We discuss the notion of criticality of semilinear differential equations and systems, its relations to scaling transformations and the Noether approach to Pokhozhaev's identities. For this purpose we propose a definition for criticality based on the S. Lie symmetry theory. We show that this definition is compatible with the well-known notion of critical exponent by considering various examples. We also review some related recent papers. We wish to thank the referees for their useful suggestions. Yuri Bozhkov is grateful to the Organizers of the 7th International Conference “Symmetry in Nonlinear Mathematical Physics”, June 24–30 2007, Kyiv, Ukraine, for having given him the opportunity to present a talk on this subject. He would also like to thank FAPESP, CNPq and FAEPEX-UNICAMP, Brasil, as well as ICTP, Trieste, Italy, for financial support. Enzo Mitidieri acknowledges the support of INTAS-05-100000B-792. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Lie Symmetries and Criticality of Semilinear Differential Systems Article published earlier |
| spellingShingle | Lie Symmetries and Criticality of Semilinear Differential Systems Bozhkov, Y. Mitidieri, E. |
| title | Lie Symmetries and Criticality of Semilinear Differential Systems |
| title_full | Lie Symmetries and Criticality of Semilinear Differential Systems |
| title_fullStr | Lie Symmetries and Criticality of Semilinear Differential Systems |
| title_full_unstemmed | Lie Symmetries and Criticality of Semilinear Differential Systems |
| title_short | Lie Symmetries and Criticality of Semilinear Differential Systems |
| title_sort | lie symmetries and criticality of semilinear differential systems |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/147807 |
| work_keys_str_mv | AT bozhkovy liesymmetriesandcriticalityofsemilineardifferentialsystems AT mitidierie liesymmetriesandcriticalityofsemilineardifferentialsystems |