Ground state solutions for quasilinear Schrödinger systems

This paper is concerned with the quasilinear Schrödinger systems in RNRN:{−Δu+(λa(x)+1)u−12(Δ|u|2)u=2αα+β|u|α−2|v|βu,−Δv+(λb(x)+1)v−12(Δ|v|2)v=2βα+β|u|α|v|β−2v,u(x)→0,v(x)→0as|x|→∞, where λ>0λ>0 is a parameter, α>2α>2, β>2β>2, α+β<2⋅2⁎α+β<2⋅2⁎ and 2⁎=2NN−2 for N⩾3N⩾3, 2⁎=+∞2⁎=+∞ for N=1,2N=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)}=intb−1(0) for λ large enough.