学术报告三十一:杨健夫—Normalized solutions and mass concentration for supercritical nonlinear Schrödinger equations

发布时间:2019-10-23

报告时间20191025日(星期五)10:30-11:30

报告地点:翡翠湖校区科教楼B1710

报告人:杨健夫教授

工作单位江西师范大学数学与信息科学学院

  

报告题目:Normalized solutions and mass concentration for supercritical nonlinear Schrödinger equations

  

报告人简介:杨健夫,二级教授,博士生导师。2001年入选中国科学院“百人计划”,首批入选赣鄱555计划。现为《Acta Mathematica Scientia》和《数学物理学报》常务编委,江西省人民政府学科评议专家,江西省数学会理事长,国家科学技术进步奖评审专家,国家自然科学基金会评专家,科技部国际合作项目通讯评审专家。1993年起享受国务院特殊津贴,1998年获国家有突出贡献中青年专家称号。先后参加和主持国家科技部重大基础研究前期研究专项,国家自然科学基金重点项目,国家自然科学基金项目的研究。在Comm. Partial Differential Equations, J. Funct. Anal., Trans. Amer. Math. Soc., Ann. Inst. H. Poincaré Anal. Non Linéaire, Calc. Var. Partial Differential Equations, SIAM J. Math. Anal., J. Differential Equations等国际高水平学术期刊上发表SCI论文120余篇。

  

报告简介:In this talk, we deal with the existence and concentration of normalized solutions to the supercritical nonlinear Schr\{o}dinger equation

-\Delta u + V(x) u = \mu_q u + a|u|^q u \q in \mathbb{R}^2,

\int_{\mathbb{R}^2}|u|^2\,dx =1,\\

where $\mu_q$ is the Lagrange multiplier. We show that for q>2 close to 2,problem \eqref{eq:0.1} admits two solutions: one is the local minimal solution $u_q$ and

another one is the mountain pass solution $v_q$. Furthermore, we study the limiting behavior of $u_q$ and $v_q$ when $q\to 2_+$. Particularly, we describe precisely the blow-up formation of the excited state $v_q$.