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王志强教授学术报告会
发布时间:2016-12-30   浏览次数:  

报告人简介:王志强美国犹他州立大学和天津大学应用数学中心教授。1982年毕业吉林大学,1984和1986年中科院数学所分别获硕士和博士学位 1986-1991年北京大学纽约大学柯朗研究所犹他大学和威斯康辛大学开展博士后工作和访问研究1991年犹他州立大学助教授,1994年副教授,1998年终身教授至今2014天津大学国家千人计划特聘教授。研究领域为非线性泛函分析和非线性微分方程,2015年当选美国数学会会士。


报告一: Localized nodal solutions for semiclassical nonlinear Schrödinger equations

(半经典非线性薛定谔方程的局部结点解)

报告时间:20171月3日(周二)9:30-11:30

报告地点:理学院二楼会议室

Abstract: We discuss the existence of localized sign-changing solutions for the semiclassical nonlinear Schrödinger equation with the potential $V$ assumed to be bounded and bounded away from zero. When V has a local minimum point $P$, as $\epsilon \to 0$, we construct an infinite sequence of localized sign-changing solutions clustered at $P$ and these solutions are of higher topological type in the sense that they are obtained from a minimax characterization of higher dimensional symmetric linking structure via the symmetric mountain pass theorem. Our method combines the Byeon and Wang’s penalization approach and minimax method via a variant of the classical symmetric mountain pass theorem, and is rather robust without using any non-degeneracy conditions


报告二: A class of quasilinear elliptic equations via a regularization approach

(正则化方法研究一类拟线性椭圆方程)

报告时间:20171月4日(周三)14:00-16:00

报告地点:理学院二楼会议室

Abstract: For a class of quasilinear elliptic problems including the modified nonlinear Schr\"odinger type equations, which lack both smoothness and compactness in the variational formulations, we develop a regularization approach for the existence theory. This allows us to overcome difficulties of both smoothness and compactness issues involved. By establishing convergence results we obtain existence and multiplicity results for the quasilinear equations.