Electronic Journal of Differential Equations,
Vol. 2006(2006), No. 76, pp. 1-12.
Title: Multiplicity of solutions for a class
of elliptic systems in $\mathbb{R}^N$
Author: Giovany M. Figueiredo (Univ. Federal do Para, Brazil)
Abstract:
This article concerns the
multiplicity of solutions for the system of equations
$$\displaylines{
-\Delta u + V(\epsilon x)u = \alpha |u|^{\alpha-2}u|v|^{\beta}, \cr
-\Delta v + V(\epsilon x)v = \beta |u|^{\alpha}|v|^{\beta-2}v
}$$
in $\mathbb{R}^N$, where $V$ is a positive potential.
We relate the number of solutions with the topology of the
set where $V$ attains its minimum.
The results are proved by using minimax theorems and
Ljusternik-Schnirelmann theory.
Submitted May 24, 2005. Published July 12, 2006.
Math Subject Classifications: 35J20, 35J50, 35J60.
Key Words: Variational methods; Palais-Smale condition;
Ljusternik-Schnirelmann theory.