Generalized Chern-Simons-Schrodinger system with critical exponential growth: the zero mass case

We consider the existence of ground state solutions for a class of zero-mass Chern-Simons-Schr\"{o}dinger systems \[ \{ {array}{ll} -Δ u +A_0 u+∑ⱼ₌₁^2A_j^2 u=f(u)-a(x)|u|ᵖ⁻²u, ∂_1A_2-∂_2A_1=-1/2|u|^2,~∂_1A_1+∂_2A_2=0, ∂_1A_0=A_2|u|^2,~ ∂_2A_0=-A_1|u|^2, {array} . \] where a: R²→ R⁺ is an external potential, p∈(1,2) and f∈ C( R) denotes a nonlinearity that fulfills the critical exponential growth in the Trudinger-Moser sense at infinity. By introducing an improvement of the version of Trudinger-Moser inequality, we are able to investigate the existence of positive ground state solutions for the given system using variational method.