Electron. J. Diff. Eqns., Vol. 2003(2003), No. 15, pp. 1-14.

A multiplicity result for a class of superquadratic Hamiltonian systems

Joao Marcos do O & Pedro Ubilla

Abstract:
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 $N\geq 1$. One solution is obtained applying Ambrosetti and Rabinowitz's classical Mountain Pass Theorem, and the other solution by a local minimization. \end{abstract}

Submitted May 15, 2002. Published February 14, 2003.
Math Subject Classifications: 35J50, 35J60, 35J65, 35J55.
Key Words: Elliptic systems, minimax techniques, Mountain Pass Theorem, Ekeland's variational principle, multiplicity of solutions.

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Joao Marcos do O
Departamento de Matematica
Universidade Federal da Paraiba
58059.900 Joao Pessoa, Pb Brazil
e-mail: jmbo@mat.ufpb.br
Pedro Ubilla
Universidad de Santiago de Chile
Cassilla 307, Correo 2, Santiago, Chile
e-mail: pubilla@lauca.usach.cl

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