报告题目：Nonlocal planar Schrödinger-Poisson systems in the fractional Sobolev limiting case

报告人：中国地质大学（武汉）刘志苏教授

报告时间：2023年9月14日10:00-11:00

地点：立志楼A422

摘要：In this talk, we introduce the nonlinear Schrödinger equation for the s−fractional p−Laplacian

strongly coupled with the Poisson equation in dimension two and with p = 2/s , which is the limiting case for the embedding of the fractional Sobolev space. We prove existence of solutions by means of a variational approximating procedure for an auxiliary Choquard equation in which the uniformly approximated sign-changing logarithmic kernel competes with the exponential nonlinearity. Qualitative properties of solutions such as symmetry and decay are also established by exploiting a suitable moving planes technique.

刘志苏：中国地质大学（武汉）数理学院特任教授，意大利因苏布利亚大学博士后、国防科技大学博士后，曾访问中科院数学与系统科学研究院，香港理工大学等。研究方向是非局部椭圆偏微分方程中的变分问题以及多智能体系统的集群稳定性问题。在国内外学术刊物上发表SCI 论文40余篇，部分研究成果发表在 J. Dif erentai Equations, Calc. Var. PDE, Ann. Mat. Pura Appl, Nonlinearity, Israel J. Math, Proc.Roy.Soc.Edinburgh Sect A, J.Geom.Anal.等国际数学刊物上,3 篇高被引论文，1 篇热点论文。现为德国 Zentralblatt MATH 评论员，美国数学评论员，国际差分方程协会会员。