Ground states for a class of quasilinear elliptic systems with critical exponent

Abstract

We study the following coupled system of quasilinear equations: −Δpu+μ|u|p−2u=|u|q−2u+αλ|u|α−2u|v|β,x∈RN,−Δpv+ν|v|p−2v=|v|p∗−2v+βλ|u|α|v|β−2v,x∈RN,where N≥3, μ,ν,λ>0, α,β≥1, 2<p<q<p∗ and α+β=p. We establish some results about the existence and regularity of ground state solutions for the p-Laplacian systems by using variational methods. We also study the asymptotic behavior of solutions as the coupling parameter λ tends to zero.