On semiclassical ground states for Hamiltonian elliptic system with critical growth
On semiclassical ground states for Hamiltonian elliptic system with critical growth
In this paper, we study the following Hamiltonian elliptic system with gradient term and critical growth: \begin{equation*} \begin{cases} -\epsilon^{2}\Delta \psi +\epsilon b\cdot \nabla \psi +\psi=K(x)f(|\eta|)\varphi+W(x)|\eta|^{2^*-2}\varphi &\hbox{in} \mathbb{R}^{N},\\ -\epsilon^{2}\Delta \varphi -\epsilon b\cdot \nabla \varphi +\varphi=K(x)f(|\eta|)\psi+W(x)|\eta|^{2^*-2}\psi &\hbox{in} \mathbb{R}^{N}, \end{cases} \end{equation*} where $\eta=(\psi,\varphi)\colon \mathbb{R}^{N}\rightarrow\mathbb{R}^{2}$, $K, W\in C(\mathbb{R}^{N}, \mathbb{R})$, $\epsilon$ is a small positive …