Multiplicity of solutions for a class of elliptic systems in ℝN

Abstract

This article concerns the multiplicity of solutions for the system of equations -Δu + V(∊x)u = α|u|α-2 u|v|β, -Δv + V(∊x)v = β|u|α|v|β-2v in ℝN, 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.