Uniqueness of least energy solutions to the fractional Lane-Emden equation in the ball

We prove uniqueness of least energy solutions to the fractional Lane-Emden equation, under homogeneous Dirichlet exterior conditions, when the underlying domain is a ball B subset of RN\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$B \subset \mathbb {R}<^>N$$\end{document}. The equation is characterized by a superlinear, subcritical power-like nonlinearity. The proof makes use of Morse theory and is inspired by some results obtained by C. S. Lin in the '90s. A new Hopf's Lemma-type result shown in this paper is an essential element in the proof of nondegeneracy of least energy solutions.