Uniqueness of least-energy solutions to the fractional Lane-Emden equation in the ball
数学专题报告
报告题目(Title)：Uniqueness of least-energy solutions to the fractional Lane-Emden equation in the ball
报告人(Speaker)：Azahara DeLaTorre (Sapienza Universita di Roma)
地点(Place)：Zoom ID：996 1061 1987, PWD: 671240
时间(Time)：2024 年 9月 12日 16：00—17：00
邀请人(Inviter)：熊金钢
报告摘要
In this talk we will show the uniqueness of least-energy solutions for the fractional Lane-Emden equation posed in the ball under homogeneous Dirichlet exterior conditions. This is a non-local semilinear equation with a superlinear and subcritical nonlinearity. Existence of positive solutions follows easily from variational methods, but uniqueness is quite complicated. In the local case, the uniqueness of positive solutions follows from the result of Gidas, Ni and Nirenberg. Indeed, by using the moving plane method, they proved radial symmetry of the solutions which allows the application of ODE techniques. In the non-local case, these arguments don't seem to work. Our proof makes use of Morse theory, and it is inspired by some results obtained by C. S. Lin in the '90s. The talk is based on a joint work with Enea Parini.
* This PDE seminar is co-organized with Tianling Jin at HKUST and Juncheng Wei at CUHK. See the seminar webpage: https://www.math.hkust.edu.hk/~tianlingjin/PDEseminar.html
