Uniqueness of least energy solutions to the fractional Lane-Emden equation in the ball
Fuente:
arXiv
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2023
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866916216019353600 |
|---|---|
| author | DelaTorre, Azahara Parini, Enea |
| author_facet | DelaTorre, Azahara Parini, Enea |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2310_02228 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Uniqueness of least energy solutions to the fractional Lane-Emden equation in the ball DelaTorre, Azahara Parini, Enea Analysis of PDEs 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. |
| title | Uniqueness of least energy solutions to the fractional Lane-Emden equation in the ball |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2310.02228 |