Stability of Standing Waves for the Nonlinear Fractional Schrödinger Equation

We study the standing waves of the nonlinear fractional Schrödinger equation. We obtain that when 0<γ<2s\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$0<\gamma <2s$$\end{document}, the standing waves are orbitally stable; when γ=2s\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\gamma =2s$$\end{document}, the ground state solitary waves are strongly unstable to blow-up.