Multiplicity of solutions for gradient systems
We establish the existence of nontrivial solutions for an elliptic system which is resonant both at the origin and at infinity. The resonance is given by an eigenvalue problem with indefinite weight, and the nonlinear term is permitted to be unbounded. Also, we consider the case where the resona...
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| Format: | Article |
| Language: | English |
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Texas State University
2010-05-01
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| Series: | Electronic Journal of Differential Equations |
| Subjects: | |
| Online Access: | http://ejde.math.txstate.edu/Volumes/2010/64/abstr.html |
| _version_ | 1830208963779493888 |
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| author | Edcarlos D. Da Silva |
| author_facet | Edcarlos D. Da Silva |
| author_sort | Edcarlos D. Da Silva |
| collection | DOAJ |
| description | We establish the existence of nontrivial solutions for an elliptic system which is resonant both at the origin and at infinity. The resonance is given by an eigenvalue problem with indefinite weight, and the nonlinear term is permitted to be unbounded. Also, we consider the case where the resonance at infinity and at the origin can occur with different weights. Our main tool is the computation of critical groups. |
| first_indexed | 2024-12-18T04:58:41Z |
| format | Article |
| id | doaj.art-449fa47047d84a2fa994743b23cacab3 |
| institution | Directory Open Access Journal |
| issn | 1072-6691 |
| language | English |
| last_indexed | 2024-12-18T04:58:41Z |
| publishDate | 2010-05-01 |
| publisher | Texas State University |
| record_format | Article |
| series | Electronic Journal of Differential Equations |
| spelling | doaj.art-449fa47047d84a2fa994743b23cacab32022-12-21T21:20:12ZengTexas State UniversityElectronic Journal of Differential Equations1072-66912010-05-01201064,115Multiplicity of solutions for gradient systemsEdcarlos D. Da SilvaWe establish the existence of nontrivial solutions for an elliptic system which is resonant both at the origin and at infinity. The resonance is given by an eigenvalue problem with indefinite weight, and the nonlinear term is permitted to be unbounded. Also, we consider the case where the resonance at infinity and at the origin can occur with different weights. Our main tool is the computation of critical groups.http://ejde.math.txstate.edu/Volumes/2010/64/abstr.htmlCritical groupsresonanceindefinite weightsMorse theory |
| spellingShingle | Edcarlos D. Da Silva Multiplicity of solutions for gradient systems Electronic Journal of Differential Equations Critical groups resonance indefinite weights Morse theory |
| title | Multiplicity of solutions for gradient systems |
| title_full | Multiplicity of solutions for gradient systems |
| title_fullStr | Multiplicity of solutions for gradient systems |
| title_full_unstemmed | Multiplicity of solutions for gradient systems |
| title_short | Multiplicity of solutions for gradient systems |
| title_sort | multiplicity of solutions for gradient systems |
| topic | Critical groups resonance indefinite weights Morse theory |
| url | http://ejde.math.txstate.edu/Volumes/2010/64/abstr.html |
| work_keys_str_mv | AT edcarlosddasilva multiplicityofsolutionsforgradientsystems |