Geodesic
A multiplicity result for a class of superquadratic Hamiltonian systems
Electronic journal of differential equations, Tome 2003 (2003)
We establish the existence of two nontrivial solutions to semilinear elliptic systems with superquadratic and subcritical growth rates. For a small positive parameter

$\displaylines{ -\Delta v = \lambda f(u) \quad \hbox{in } \Omega , \cr -\Delta u = g(v) \quad \hbox{in } \Omega , \cr u = v=0 \quad \hbox{on } \partial \Omega , }$

where $\Omega$ is a smooth bounded domain in $\mathbb{R}^N$ with $N\geq 1$. One solution is obtained applying Ambrosetti and Rabinowitz's classical Mountain Pass Theorem, and the other solution by a local minimization. endabstract
Classification : 35J50, 35J60, 35J65, 35J55
Keywords: elliptic systems, minimax techniques, mountain pass theorem, ekeland's variational principle, multiplicity of solutions 
@article{EJDE_2003__2003__a50,
     author = {Marcos do \'O,  Jo\~ao and Ubilla,  Pedro},
     title = {A multiplicity result for a class of superquadratic {Hamiltonian} systems},
     journal = {Electronic journal of differential equations},
     year = {2003},
     volume = {2003},
     zbl = {1034.35046},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2003__2003__a50/}
}
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AU  - Ubilla,  Pedro
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%A Marcos do Ó,  João
%A Ubilla,  Pedro
%T A multiplicity result for a class of superquadratic Hamiltonian systems
%J Electronic journal of differential equations
%D 2003
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%U http://geodesic.mathdoc.fr/item/EJDE_2003__2003__a50/
%G en
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Marcos do Ó,  João; Ubilla,  Pedro. A multiplicity result for a class of superquadratic Hamiltonian systems. Electronic journal of differential equations, Tome 2003 (2003). http://geodesic.mathdoc.fr/item/EJDE_2003__2003__a50/