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数学学科现代分析及其应用研究所学术报告(刘嘉荃 北京大学)

发布者:付慧娟   发布时间:2019-12-31  浏览次数:267


报告题目:Localized nodal solutions for a critical nonlinear Schr?dinger equation

报 人:刘嘉荃教授北京大学



Abstract: For semiclassical nonlinear Schr?dinger equations with Sobolev critical exponent we propose and implement a procedure to construct an unbounded sequence of semiclassical bound states which are localized nodal solutions and are concentrated at a local minimum set of the potential. Our approach does not need any non-degeneracy condition of the limiting equation and is robust for more general problems.


报告题目:Localized nodal solutions for quasilinear Schr?dinger equation

报 人:刘嘉荃教授北京大学



Abstract: We establish for small εthe existence of a sequence of localized nodal solutions concentrating near a given local minimum point of the potential function, by developing new variational perturbation method to treat this class of non-smooth variational problems. The new method allows the perturbed variational functionals to share critical points with the original functional. This method allows us to avoid any limiting process from the perturbed problems to the original problem, and it is effective in dealing with multiple existence of solutions.

报告人概况:刘嘉荃,北京大学教授、博士生导师。刘教授工作经历丰富,成就斐然,是我国非线性分析领域的著名专家。刘嘉荃教授一直从事非线性泛函分析及其对微分方程的应用方面的研究,在国际一流Top期刊上发表多篇学术论文,并有多部非线性泛函方面的著作一直被各高校选作研究生教材。代表作多发在:J. Functional AnalysisAnnales de l Institut Henri Poincare (C) Analyse non lineaireCalculus of Variations & Partial Differential  EquationsJournal of Differential EquationsCommunications in Contemporary  MathematicsCommu. PDEMath. ZeitschriftJournal of the London  Mathematical Society等国际著名学术期刊。


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