Speaker: Florica C. Cirstea (悉尼大学)
Time: 2026-01-30 13:30-17:30
Location: 1110, SIMIS
摘要：
In this talk, we present new results on the existence and classification of the behaviour near zero of the positive $C^2(B_R(0)\setminus \{0\})$ solutions of
$$ -\Delta u = \frac{u^{2^\star(s)-1}}{|x|^s} – \mu \frac{u^q}{|x|^\tau} \quad \text{in } B_R(0)\setminus\{0\},
$$ where $B_R(0)$ is the open ball in $\mathbb R^n$ centered at $0$ and of radius $R>0$. Here, $n\geq 3$, $q>1$, $\mu>0$, $\tau\in \mathbb R$, $s\in (0,2)$ and $2^*(s)=2(n-s)/(n-2)$. The classification of singularities is intimately connected with the position of $\tau$ with respect to $2$, as well as $s$. We will focus on the case of removable singularities to emphasize the changes between $\tau<2$ and $\tau\geq 2$. We will also examine certain singular asymptotic profiles using Pohozaev type arguments. We use a dynamical systems approach to obtain the existence of solutions with the desired profile.
This talk is based on joint works with F. Robert, J. Vétois and H. Wondo.
About Speaker:
Florica C. Cirstea，悉尼大学教授，博士生导师，主要从事偏微分方程的研究，对拟线性问题做了一系列重要的工作。在Anal. PDE, Math. Ann., Ann. Inst. H. Poincare–AN, Comm. PDE, Proc. LMS, Trans. AMS, JMPA, JFA, CVPDE等国际数学顶尖杂志发表SCI学术论文43篇。
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