A multiplicity result for a class of superquadratic Hamiltonian systems
We establish the existence of two nontrivial solutions to semilinear elliptic systems with superquadratic and subcritical growth rates. For a small positive parameter $ lambda $, we consider the system $$displaylines{ -Delta v = lambda f(u) quad hbox{in } Omega , cr -Delta u = g(v) quad hbox{in } Om...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Texas State University
2003-02-01
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| Series: | Electronic Journal of Differential Equations |
| Subjects: | |
| Online Access: | http://ejde.math.txstate.edu/Volumes/2003/15/abstr.html |
| _version_ | 1818236103799341056 |
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| author | Joao Marcos Do O Pedro Ubilla |
| author_facet | Joao Marcos Do O Pedro Ubilla |
| author_sort | Joao Marcos Do O |
| collection | DOAJ |
| description | We establish the existence of two nontrivial solutions to semilinear elliptic systems with superquadratic and subcritical growth rates. For a small positive parameter $ lambda $, we consider the system $$displaylines{ -Delta v = lambda f(u) quad hbox{in } Omega , cr -Delta u = g(v) quad hbox{in } Omega , cr u = v=0 quad hbox{on } partial Omega , }$$ where $Omega$ is a smooth bounded domain in $mathbb{R}^N$ with $Ngeq 1$. One solution is obtained applying Ambrosetti and Rabinowitz's classical Mountain Pass Theorem, and the other solution by a local minimization. end{abstract} |
| first_indexed | 2024-12-12T12:04:33Z |
| format | Article |
| id | doaj.art-fbc114bcf25b4846a8f40fdb7967ce1d |
| institution | Directory Open Access Journal |
| issn | 1072-6691 |
| language | English |
| last_indexed | 2024-12-12T12:04:33Z |
| publishDate | 2003-02-01 |
| publisher | Texas State University |
| record_format | Article |
| series | Electronic Journal of Differential Equations |
| spelling | doaj.art-fbc114bcf25b4846a8f40fdb7967ce1d2022-12-22T00:25:01ZengTexas State UniversityElectronic Journal of Differential Equations1072-66912003-02-01200315114A multiplicity result for a class of superquadratic Hamiltonian systemsJoao Marcos Do OPedro UbillaWe establish the existence of two nontrivial solutions to semilinear elliptic systems with superquadratic and subcritical growth rates. For a small positive parameter $ lambda $, we consider the system $$displaylines{ -Delta v = lambda f(u) quad hbox{in } Omega , cr -Delta u = g(v) quad hbox{in } Omega , cr u = v=0 quad hbox{on } partial Omega , }$$ where $Omega$ is a smooth bounded domain in $mathbb{R}^N$ with $Ngeq 1$. One solution is obtained applying Ambrosetti and Rabinowitz's classical Mountain Pass Theorem, and the other solution by a local minimization. end{abstract}http://ejde.math.txstate.edu/Volumes/2003/15/abstr.htmlElliptic systemsminimax techniquesMountain Pass TheoremEkeland's variational principle |
| spellingShingle | Joao Marcos Do O Pedro Ubilla A multiplicity result for a class of superquadratic Hamiltonian systems Electronic Journal of Differential Equations Elliptic systems minimax techniques Mountain Pass Theorem Ekeland's variational principle |
| title | A multiplicity result for a class of superquadratic Hamiltonian systems |
| title_full | A multiplicity result for a class of superquadratic Hamiltonian systems |
| title_fullStr | A multiplicity result for a class of superquadratic Hamiltonian systems |
| title_full_unstemmed | A multiplicity result for a class of superquadratic Hamiltonian systems |
| title_short | A multiplicity result for a class of superquadratic Hamiltonian systems |
| title_sort | multiplicity result for a class of superquadratic hamiltonian systems |
| topic | Elliptic systems minimax techniques Mountain Pass Theorem Ekeland's variational principle |
| url | http://ejde.math.txstate.edu/Volumes/2003/15/abstr.html |
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