报告题目1：非线性薛定谔方程基态解的新进展

报告人：马力教授，北京科技大学

报告时间：2025年12月22日（周一）14:00-16:00

报告地点：20-306

报告摘要：为了理解量子现象，数学和物理上有大量文献研究了非线性薛定谔方程和分数阶的非线性薛定谔方程。本讲座讨论在两种位势条件下，全空间上非线性薛定谔方程基态解的存在性问题。我们涉及的方面有：1：证明在这两种情形下，用对应泛函的自然定义出的Hilbert空间和Sobolev $H^1$空间是一致的。2：采用Nehari流形的方法和集中紧性来克服非紧区域带来的困难。

报告题目2：Profile decomposition of the bounded sequence for nonlinear nonlocal elliptic equations

报告人：马力教授，北京科技大学

报告时间：2025年12月23日（周二）14:00-16:00

报告地点：20-306

报告摘要：In this talk, we consider profile decomposition of the bounded sequence in the space H^s, s>0, for semilinear elliptic equations of local type or non-local type, which are the stationary nonlinear Schrodinger equations on the whole space. We give the full proof of the compactness lemma (due to Hmidi-Keraani when s=1), for the bounded sequence in the space $H^s$. As we may see, the Gagliardo-Nirenberg inequality plays an important role in the argument. This result is very useful in the blow-up theory of the nonlinear nonlocal Schrodinger equations.

报告题目3：Ground states of Schrodinger-Poisson-Slatter equations with linear non-local terms

报告人：马力教授，北京科技大学

报告时间：2025年12月24日（周三）14:00-16:00

报告地点：20-306

报告摘要：We study the nonlocal Schrodinger-Poisson-Slater type equation with nonlocal linear term, which is the case not studied by others before. The non-local linear term is usually defined by Riesz potential or Bessel potential and their physical meaning is not just for mass assembling. We prove existence results of radial groundstates in some cases and our method is based on the Nehari method.

报告题目4：Schrodinger-Poisson-Slatter equations with critical exponents

报告人：马力教授，北京科技大学

报告时间：2025年12月25日（周四）14:00-16:00

报告地点：20-306

报告摘要：We address the following semilinear elliptic problem with critical exponent and with non-local linear term. The non-local linear term is defined by the Riesz potential of solutions on the bounded domain of the whole Eiclidean space. We study the non-existence, existence and multiplicity results. Our problem under study is of Brezis-Nirenberg type and we need to consider the interaction between bubbles. The regularity results of the eigenvalue problem involving Riesz potential terms will be used. The talk is based on the joint work with Haoyu Li.

系列报告人简介：马力，北京科技大学教授，博士生导师。1989年博士毕业于中国科学院数学所，师从王光寅研究员和丁伟岳；1991年北京大学数学系博士后出站，合作导师张恭庆。马力教授主要从事几何分析和非线性分析、偏微分方程的研究。近期在黎曼几何的重要问题，比如Yamabe流、Ricci流等方面，取得了一系列重要的研究成果。在Adv. Math., J. Math. Pures Appl., Arch. Ration. Mech. Anal., J. Funct. Anal., JDE, Comm. Math. Phy., CVPDE等著名学术期刊上发表多篇论文。长期担任两个国际数学SCI杂志(AGAG, JPDOA)编委。

邀请人：非线性分析与PDE团队