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

Abstract We study the following coupled system of quasilinear equations: − Δ p u + μ | u | p − 2 u = | u | q − 2 u + α λ | u | α − 2 u | v | β , x ∈ R N , − Δ p v + ν | v | p − 2 v = | v | p ∗ − 2 v + β λ | u | α | v | β − 2 v , x ∈ R N , 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. [ABSTRACT FROM AUTHOR]