Existence of ground state solutions to Hamiltonian elliptic system with potentials

In this paper, we investigate nonlinear Hamiltonian elliptic system

$\{\begin{array}{c}\left(-\Delta \right)u=\overrightarrow{b}\left(x\right)??u+\left(V\left(x\right)+\tau \right)u=K\left(x\right)g\left(v\right)\text{in}{?}^{?},\\ \left(-\Delta \right)v=\overrightarrow{b}\left(x\right)??v+\left(V\left(x\right)+\tau \right)v=K\left(x\right)f\left(u\right)\text{in}{?}^{?},\\ u\left(x\right)\to 0andv\left(x\right)\to 0as\left|x\right|\to \infty ,\end{array}$

where N ≥ 3, τ > 0 is a positive parameter and V, K are nonnegative continuous functions, f and g are both superlinear at 0 with a quasicritical growth at infinity. By establishing a variational setting, the existence of ground state solutions is obtained.