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.