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.