美国犹他州立大学王志强教授学术报告6月6日下午
发布时间: 2018-06-05 访问次数: 54

学术讲座【非线性椭圆边值问题的变分方法(一)】

  

时间:201866(星期三)下午14:00-15:00

  

地点:理工北楼601报告厅

  

主办:数学与信息学院, 福建省分析数学及应用重点实验室

  

主讲:美国犹他州立大学,王志强教授

  

参加对象:相关方向老师及学生


专家简介:王志强,美国犹他州立大学终身教授,现受聘天津大学教授、中组部“千人计划”。在 Morse 理论应用于椭圆边值问题,椭圆问题的单峰解、多峰解、奇异变分问题、非线性 Schrodinger  Schrodinger 方程组等不失去紧性的变分问题的研究,取得了很多重要的研究成果,是国际著名的非线性分析和偏微分方程专家。

  

报告摘要:Semilinear elliptic PDEs of second order with a term that grows superlinearly in the unknown have attracted much attention in the past decades. The field was opened up by Ambrosetti and Rabinowitz with what has become to be known as the Mountain Pass Theorem''. This topic is a review of by now classical results and of newer research in this area. The authors concentrate on homogeneous Dirichlet boundary conditions.Topics that are covered include existence and non-existence, positivity and non-positivity, symmetry and non-symmetry, uniqueness and non-uniqueness, and qualitative properties of solutions. For some of the main ideas streamlined proofs are provided, covering variants of the Mountain Pass Theorem, the Nehari manifold (also its more specialized companion, the nodal Nehari set), Morse theory, the moving plane method, and concentration compactness. A few results about parameter dependent problems are given, where in general the topology and geometry of the domain and of the sublevel sets of a can be exploited, but the authors do not try to give an account of the huge amount of literature on singularly perturbed problems..