Asymptotic profiles of ground states for Choquard equations with combined nonlinearities(II)

讲座时间 Datetime: 2021年11月2日，星期二，19:30-21:00

地点 Venue: 腾讯会议，875 618 957

报告人 Speaker:  马世旺 教授

单位 Affiliation: 南开大学

报告摘要 Abstract:

We study asymptotic behaviour of positive ground state solutions of the nonlinear  Choquard equation

$$

-\Delta v+\varepsilon v=(I_\alpha \ast |u|^{p})|v|^{p-2}v+ |v|^{q-2}v,

\quad {\rm in} \ \mathbb R^N,

 \eqno(P_\varepsilon)

 $$

where $N\ge 3$ is an integer, $p\in [\frac{N+\alpha}{N}, \frac{N+\alpha}{N-2}]$, $q\in (2,2^*)$ with $2^*=\frac{2N}{N-2}$, and  $\varepsilon>0$ is a parameters. We  show that as $\varepsilon\to 0$, after {\em a rescaling} the ground state solutions of $(P_\varepsilon)$ converge to a particular solution of some limit equations. We also establish a sharp asymptotic characterisation of such a rescaling.