Ground state solutions for quasilinear Schrِdinger systems

This paper is concerned with the quasilinear Schrödinger systems in R N : { − Δ u + ( λ a ( x ) + 1 ) u − 1 2 ( Δ | u | 2 ) u = 2 α α + β | u | α − 2 | v | β u , − Δ v + ( λ b ( x ) + 1 ) v − 1 2 ( Δ | v | 2 ) v = 2 β α + β | u | α | v | β − 2 v , u ( x ) → 0 , v ( x ) → 0 as | x | → ∞ , where λ > 0 is a parameter, α > 2 , β > 2 , α + β < 2 ⋅ 2 ⁎ and 2 ⁎ = 2 N N − 2 for N ⩾ 3 , 2 ⁎ = + ∞ for N = 1 , 2 is the critical Sobolev exponent. By using the Nehari manifold method and concentration compactness principle in the Orlicz space, we prove the existence of ground state solution which localize near the potential well int { a − 1 ( 0 ) } = int b − 1 ( 0 ) for λ large enough.