Geodesic
A multiplicity result for a class of superquadratic Hamiltonian systems
Electronic Journal of Differential Equations, Tome 2003 (2003).

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: 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},
     publisher = {mathdoc},
     volume = {2003},
     year = {2003},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2003__2003__a50/}
}
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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/