Existence and Concentrate Behavior of Schrödinger equations with critical exponential growth in $\mathbb{R}^N$ - Zhang, Jian; Zou, Wenming (Topological Methods in Nonlinear Analysis, 2016)
We consider the nonlinear Schrödinger equation \begin{equation*} -Δ u + (1+μ g(x))u = f(u) \quad \text{in } \mathbb{R}^N, \end{equation*} where $N \ge 3$, $μ \ge 0$; the function $g \ge 0$ has a potential well and $f$ has critical growth. By using variational methods, the existence and concentration behavior of the ground state solution are obtained.