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 \(B \subset \mathbb {R}^N\) $B\subset {\mathbb{R}}^N$ . 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.