Existence of solutions for perturbed elliptic system with critical exponents

摘要

In this paper, the perturbed elliptic system with critical exponents − ε 2 Δ u + V ( x ) u = f ( x , u ) + α α + β K ( x ) | u | α − 2 u | v | β $-arepsilon^{2}Delta u+V(x)u= f(x,u)+rac{lpha}{lpha+eta} K(x)|u|^{lpha-2}u|v|^{eta}$ , x ∈ R N $xin{mathbb{R}^{N}}$ , − ε 2 Δ v + V ( x ) v = g ( x , v ) + β α + β K ( x ) | u | α | v | β − 2 v $-arepsilon^{2}Delta v+V(x)v=g(x,v)+rac{eta}{lpha+eta }K(x)|u|^{lpha}|v|^{eta-2}v$ , x ∈ R N