Normalized solutions to fractional Schrödinger equation with potentials
Normalized solutions to fractional Schrödinger equation with potentials
In this paper, we utilize variational method to study the following fractional Schrödinger equation with a prescribed $ L^2 $-mass:$ \begin{equation*} \begin{cases} (-\Delta)^s u+(V(x)+\lambda)u = g(u)\;\; \hbox{in}\;\mathbb{R}^N,\\ \int_{\mathbb R^N}|u|^2 \mathrm{d} x = a. \end{cases} \end{equation*} $Here $ (-\Delta)^s $ is the fractional Laplacian operator, $ s\in(0,1) $, $ N\geq2 $, …