Transition between nonlinear and linear eigenvalue problems

主题:Transition between nonlinear and linear eigenvalue problems

主讲人:刘兆理

时间:2022-08-21 08:30:00

地点:腾讯会议 853-919-327

组织单位:非线性科学研究所、数学系

主讲人简介:

刘兆理,首都师范大学数学科学学院教授,博士生导师。从事非线性分析研究,在变分方法和椭圆型偏微分方程方面做出了多项研究成果。曾四次获得省部级自然科学奖和科技进步奖,曾获得国家杰出青年科学基金,被评为教育部“长江学者特聘教授”,曾获得首都劳动奖章。

内容摘要:

We study convergence of variational solutions of the nonlinear eigenvalue problem $$-\Delta u=\lambda|u|^{p-2}u,\ \ \ \ u\in H_0^1(\Omega),$$ as $p\downarrow2$ or as $p\uparrow2$, where $\Omega$ is a bounded domain in $\mathbb R^N$ with smooth boundary. It turns out that if $\lambda$ is not an eigenvalue of $-\Delta$ then the solutions either blow up or vanish according to $p\downarrow2$ or $p\uparrow2$, while if $\lambda$ is an eigenvalue of $-\Delta$ then the solutions converge to the associated eigenspace.

主持人:秦玉明


撰写:李学元