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 $$displaylines{ -Delta v = lambda f(u) quad hbox{in } Omega , cr -Delta u = g(v) quad hbox{in } Om...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Texas State University
2003-02-01
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| Series: | Electronic Journal of Differential Equations |
| Subjects: | |
| Online Access: | http://ejde.math.txstate.edu/Volumes/2003/15/abstr.html |
| Summary: | We establish the existence of two nontrivial solutions to semilinear elliptic systems with superquadratic and subcritical growth rates. For a small positive parameter $ lambda $, we consider the system $$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} |
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| ISSN: | 1072-6691 |