讲座题目：Elliptic equations driven by the Stuart differential operator and some perspectives
主讲人：Radulescu D. Vicentiu 教授
主持人：周风 教授
开始时间：2024-04-01 13:00
讲座地址：闵行校区数学楼401报告厅
主办单位：数学科学学院
报告人简介：
Radulescu D. Vicentiu教授，罗马尼亚科学院数学研究所。博士毕业于巴黎六大，师从世界著名偏微分方程专家Haim Brezis教授。Radulescu教授主要从事非线性椭圆方程、带退化和奇异线性的数学物理方程、非齐次微分算子的谱分析及其在电流变液中的应用等工作，出版专著10余部，在国际著名期刊上发表高水平的学术论文近500篇，多次主持罗马尼亚国家科学研究委员会科研项目。Radulescu教授是Thomson Reuters高被引研究者，论文被引用次数高达11000余次，应邀主题发言、大会报告和邀请报告50余次，得到了国际学术界的高度认可，并作为大会主席组织了多个专题国际学术大会，同时担任多个国际SCI期刊的主编或编委。
报告内容：
We are concerned with a class of second order quasilinear elliptic equations driven by a nonhomogeneous differential operator introduced by C.A. Stuart and whose study is motivated by models in Nonlinear Optics. We establish sufficient conditions for the existence of at least one or two non-negative solutions. Our analysis considers the cases when the reaction has either a sublinear or a linear growth. In the sublinear case, we also prove a nonexistence property. The second part of this paper is devoted to subcritical and critical cases for problems with lack of compactness. Some perspectives around this new topic are developed during this talk.
