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arXiv · 2310.02228

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

Azahara DelaTorre·Enea Parini
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Abstract

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

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Azahara DelaTorre, Enea Parini. 2023-10-03. Uniqueness of least energy solutions to the fractional Lane-Emden equation in the ball. https://arxiv.org/abs/2310.02228

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