Concentration Behavior of Ground States for $L^2$-Critical Schrödinger Equation with a Spatially Decaying Nonlinearity

Yong Luo, Shu Zhang

We consider the following time-independent nonlinear $L^2$-critical Schrödinger equation \[ -Δu(x)+V(x)u(x)-a|x|^{-b}|u|^{1+\frac{4-2b}{N}}=μu(x)\,\ \hbox{in}\,\ \mathbb{R}^N, \] w…