In this paper, we consider the system 8>>< >>: −p(x)u + |u|p(x)−2u = a(x)|u|r1(x)−2u + (x) (x)+ (x) c(x)|u| (x)−2u|v| (x) in −q(x)v + |v|q(x)−2v = μb(x)|v|r2(x)−2v + (x) (x)+ (x) c(x)|v| (x)−2v|u| (x) in @u @ = @v @ = 0 on @ where RN is a bounded domain with smooth boundary and , μ > 0, is the outer unit normal to @ . Under suitable assumptions, we prove the existence of positive solutions by using the Nehari manifold and some variational techniques.
