Electronic Journal of Differential Equations,
Vol. 2003(2003), No. 15, pp. 1-14.

Title: A multiplicity result for a class of superquadratic Hamiltonian systems

Authors: Joao Marcos do O (Univ. Fed. Paraiba, Brazil)
         Pedro Ubilla (Univ. de Santiago de Chile, Chile)

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.