Electron. J. Diff. Eqns., Vol. 2006(2006), No. 76, pp. 1-12.

Multiplicity of solutions for a class of elliptic systems in $\mathbb{R}^N$

Giovany M. Figueiredo

This article concerns the multiplicity of solutions for the system of equations
 -\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.

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Giovany M. Figueiredo
Universidade Federal do Pará
Departamento de Matemática
CEP: 66075-110 Belém - Pa, Brazil
email: giovany@ufpa.br

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